read0191077/published_papers/50723165 Toru Hasunuma Exponentiation of Graphs. Mathematics in Computer Science 19 5 1 25 20250600 10.1007/s11786-025-00609-1 read0191077/published_papers/50723164 Toru Hasunuma Connectivity Preserving Hamiltonian Cycles in k-Connected Dirac Graphs. Graphs and Combinatorics 41 10 1 22 20250200 10.1007/s00373-024-02874-6 read0191077/published_papers/47509726 Toru Hasunuma Completely Independent Spanning Trees in Line Graphs. Graphs and Combinatorics 39 90 1 16 20230800 10.1007/s00373-023-02688-y read0191077/published_papers/47509727 Toru Hasunuma Connectivity preserving trees in k-connected or k-edge-connected graphs. Journal of Graph Theory 102 3 423 435 20230000 10.1002/jgt.22878 read0191077/published_papers/47509729 Toru Hasunuma Augmenting a Tree to a k-Arbor-Connected Graph with Pagenumber k. Springer Combinatorial Algorithms - 32nd International Workshop(IWOCA) 356 369 20210000 10.1007/978-3-030-79987-8_25 read0191077/published_papers/47509728 Toru Hasunuma Connectivity Keeping Trees in 2-Connected Graphs with Girth Conditions. Algorithmica 83 9 2697 2718 20210000 10.1007/s00453-021-00833-8 read0191077/published_papers/47509731 Toru Hasunuma Connectivity Keeping Trees in 2-Connected Graphs with Girth Conditions. Springer Combinatorial Algorithms - 31st International Workshop(IWOCA) 316 329 20200000 10.1007/978-3-030-48966-3_24 read0191077/published_papers/47509730 Toru Hasunuma Kosuke Ono Connectivity keeping trees in 2-connected graphs. Journal of Graph Theory 94 1 20 29 20200000 10.1002/jgt.22504 read0191077/published_papers/15448062 Toru Hasunuma Constructions of universalized Sierpiński graphs based on labeling manipulations Constructions of universalized Sierpiński graphs based on labeling manipulations. Elsevier B.V. Electronic Notes in Discrete Mathematics 1571-0653 60 47 54 20170701 10.1016/j.endm.2017.06.007 2-s2.0-85021443142 read0191077/published_papers/15448064 Toru Hasunuma Minimum degree conditions and optimal graphs for completely independent spanning trees Springer Verlag Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 1611-3349 9538 260 273 20160000 10.1007/978-3-319-29516-9_22 2-s2.0-84961223461 read0191077/published_papers/15448063 Toru Hasunuma Structural properties of subdivided-line graphs Elsevier Journal of Discrete Algorithms 1570-8667 31 69 86 20150301 10.1016/j.jda.2015.01.008 2-s2.0-84923339316 read0191077/published_papers/26502823 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno Algorithmic aspects of distance constrained labeling: a survey. IJNC 4 2 251 259 20140000 10.15803/ijnc.4.2_251 read0191077/published_papers/15448065 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno A Linear Time Algorithm for L(2,1)-Labeling of Trees ALGORITHMICA 0178-4617 66 3 654 681 20130700 10.1007/s00453-012-9657-z read0191077/published_papers/15448066 Toru Hasunuma Structural properties of subdivided-line graphs Springer Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 0302-9743 8288 216 229 20130000 10.1007/978-3-642-45278-9_19 2-s2.0-84893115000 read0191077/published_papers/15448070 Toru Hasunuma Chie Morisaka Completely independent spanning trees in torus networks NETWORKS 0028-3045 60 1 59 69 20120800 10.1002/net.20460 read0191077/published_papers/15448067 Toru Hasunuma Mayu Otani On the (h, k)-domination numbers of iterated line digraphs DISCRETE APPLIED MATHEMATICS 0166-218X 160 12 1859 1863 20120800 10.1016/j.dam.2012.03.024 read0191077/published_papers/15448069 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno A tight upper bound on the (2, 1)-total labeling number of outerplanar graphs Journal of Discrete Algorithms 1570-8667 14 189 206 20120700 10.1016/j.jda.2011.12.020 2-s2.0-84860841442 read0191077/published_papers/15448068 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno The (p, q)-total labeling problem for trees DISCRETE MATHEMATICS 0012-365X 312 8 1407 1420 20120400 10.1016/j.disc.2012.01.007 read0191077/published_papers/15448073 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno The (2,1)-Total Labeling Number of Outerplanar Graphs Is at Most Delta+2 The (2, 1)-Total Labeling Number of Outerplanar Graphs Is at Most Δ + 2. COMBINATORIAL ALGORITHMS Combinatorial Algorithms - 21st International Workshop, IWOCA 2010, London, UK, July 26-28, 2010, Revised Selected Papers 0302-9743 6460 103 + 20110000 10.1007/978-3-642-19222-7_11 read0191077/published_papers/15448071 Toru Hasunuma Hiroshi Nagamochi Improved Bounds for Minimum Fault-Tolerant Gossip Graphs GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE 0302-9743 6986 203 + 20110000 10.1007/978-3-642-25870-1_19 read0191077/published_papers/15448072 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno The (p, q)-total Labeling Problem for Trees ALGORITHMS AND COMPUTATION, PT 2 0302-9743 6507 49 + 20100000 10.1007/978-3-642-17514-5_5 read0191077/published_papers/15448075 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno An O(n(1.75)) algorithm for L(2,1)-labeling of trees THEORETICAL COMPUTER SCIENCE 0304-3975 410 38-40 3702 3710 20090900 10.1016/j.tcs.2009.04.025 read0191077/published_papers/15448074 Toru Hasunuma Improved book-embeddings of incomplete hypercubes DISCRETE APPLIED MATHEMATICS 0166-218X 157 7 1423 1431 20090400 10.1016/j.dam.2008.10.008 read0191077/published_papers/15448076 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno A Linear Time Algorithm for L(2,1)-Labeling of Trees ALGORITHMS - ESA 2009, PROCEEDINGS 0302-9743 5757 35 + 20090000 10.1007/978-3-642-04128-0_4 read0191077/published_papers/15448077 Toru Hasunuma Toshimasa Ishii Hirotaka Ono Yushi Uno An O(n<(1.75)) algorithm for L(2,1)-labeling of trees ALGORITHM THEORY - SWAT 2008 0302-9743 5124 185 + 20080000 10.1007/978-3-540-69903-3_18 read0191077/published_papers/15467030 Toru Hasunuma Misa Hirota An improved upper bound on the queuenumber of the hypercube INFORMATION PROCESSING LETTERS 0020-0190 104 2 41 44 20071000 10.1016/j.ipl.2007.05.006 read0191077/published_papers/15448078 Toru Hasunuma Queue layouts of iterated line directed graphs DISCRETE APPLIED MATHEMATICS 0166-218X 155 9 1141 1154 20070500 10.1016/j.dam.2006.04.045 read0191077/published_papers/50723369 Toru Hasunuma Multilayer Grid Embeddings of Iterated Line Digraphs. Australian Computer Society Theory of Computing 2006(CATS) 21 26 20060000 read0191077/published_papers/15467031 T Hasunuma Y Kikuchi T Mori Y Shibata On the number of cycles in generalized Kautz digraphs DISCRETE MATHEMATICS 0012-365X 285 1-3 127 140 20040800 10.1016/j.disc.2004.01.014 read0191077/published_papers/15467032 T Hasunuma Laying out iterated line digraphs using queues GRAPH DRAWING 0302-9743 2912 202 213 20040000 10.1007/978-3-540-24595-7_19 read0191077/published_papers/15467033 T Hasunuma Embedding iterated line digraphs in books NETWORKS 0028-3045 40 2 51 62 20020900 10.1002/net.10032 read0191077/published_papers/15467034 T Hasunuma Completely independent spanning trees in maximal planar graphs GRAPH-THEORETIC CONCEPTS IN COMPUTER SCIENCE 0302-9743 2573 235 245 20020000 10.1007/3-540-36379-3_21 read0191077/published_papers/15467035 T Hasunuma H Nagamochi Independent spanning trees with small depths in iterated line digraphs DISCRETE APPLIED MATHEMATICS 0166-218X 110 2-3 189 211 20010600 10.1016/S0166-218X(00)00269-9 read0191077/published_papers/15467036 T Hasunuma Completely independent spanning trees in the underlying graph of a line digraph DISCRETE MATHEMATICS 0012-365X 234 1-3 149 157 20010500 10.1016/S0012-365X(00)00377-0 read0191077/published_papers/15467038 H Nagamochi T Hasunuma An efficient NC algorithm for a sparse k-edge-connectivity certificate JOURNAL OF ALGORITHMS 0196-6774 38 2 354 373 20010200 10.1006/jagm.2000.1144 read0191077/published_papers/15467037 Toru Hasunuma Independent spanning cycle-rooted trees in the cartesian product of digraphs. Electronic Notes in Discrete Mathematics 7 106 109 20010000 10.1016/S1571-0653(04)00236-7 read0191077/published_papers/15467040 T Hasunuma On edge-disjoint spanning trees with small depths INFORMATION PROCESSING LETTERS 0020-0190 75 1-2 71 74 20000700 10.1016/S0020-0190(00)00078-8 read0191077/published_papers/15467039 Y Shibata T Hasunuma S Fukuda Isomorphic factorization of de Bruijn digraphs DISCRETE MATHEMATICS 0012-365X 218 1-3 199 208 20000500 10.1016/S0012-365X(99)00304-0 read0191077/published_papers/50723514 Toru Hasunuma The pagenumber of de Bruijn and Kautz digraphs Theory of Computing 1999(CATS) 232-246 1999年 null null 19990100 read0191077/published_papers/15467042 H Nagamochi T Hasunuma An efficient NC algorithm for a sparse k-edge-connectivity certificate ALGORITHMS AND COMPUTATIONS 0302-9743 1533 447 456 19980000 10.1007/3-540-49381-6_47 read0191077/published_papers/15467041 T Hasunuma H Nagamochi Independent spanning trees with small depths in iterated line digraphs PROCEEDINGS OF THE 4TH AUSTRALASIAN THEORY SYMPOSIUM, CATS'98 20 3 21 35 19980000 read0191077/published_papers/15467043 T Hasunuma Y Shibata Embedding de Bruijn, Kautz and shuffle-exchange networks in books DISCRETE APPLIED MATHEMATICS 0166-218X 78 1-3 103 116 19971000 10.1016/S0166-218X(97)00009-7 read0191077/published_papers/15467045 T Hasunuma Y Shibata Counting small cycles in generalized de Bruijn digraphs NETWORKS 0028-3045 29 1 39 47 19970100 10.1002/(SICI)1097-0037(199701)29:1<39::AID-NET4>3.0.CO;2-D read0191077/published_papers/15467044 T Hasunuma Y Shibata Containment of butterflies in networks constructed by the line digraph operation INFORMATION PROCESSING LETTERS 0020-0190 61 1 25 30 19970100 10.1016/S0020-0190(96)00183-4 read0191077/published_papers/15467047 T Hasunuma Y Shibata Remarks on the placeability of isomorphic trees in a complete graph JOURNAL OF GRAPH THEORY 0364-9024 21 1 41 42 19960100 10.1002/(SICI)1097-0118(199601)21:1<41::AID-JGT5>3.0.CO;2-M read0191077/published_papers/15467046 T Hasunuma Y Shibata The number of labeled graphs placeable by a given permutation JOURNAL OF GRAPH THEORY 0364-9024 21 1 11 19 19960100 10.1002/(SICI)1097-0118(199601)21:1<11::AID-JGT2>3.0.CO;2-P read0191077/misc/37616192 蓮沼徹石井利昌小野廣隆宇野裕之 The (p, q)-total labeling problem for trees 木の(p, q)-全ラベリング問題グラフ G の k-(p,q)-全ラベリングとは，G の節点と辺への 0 から k までの整数値の割当てであり，節点とそれに接続する辺の間では少なくとも p，隣接する 2 節点間または 2 辺間では少なくとも q の差があるもののことをいう．G の (p, q)-全ラベリング数 λTp;q(G) は，k がとりうる値の最小値として定義される．G の (p, q)-全ラベリング問題とは，ラベリング数 λTp;q(G) を求める問題である．本研究では，いくつかのグラフクラスのグラフの (p, q)-全ラベリング数に対して新しい上界と下界を与える．とくに，グラフが木の場合にはタイトな上界と下界を与える．また，グラフが木で p≦3q/2 の場合に (p, q)-全ラベリング問題を解く線形時間アルゴリズムを与え，さらに最大次数が 4 以上という仮定が加わった場合，λTp;q(T) を実現する木Tを完全に特徴づけられることも示す．この結果は，(p; q)-全ラベリング問題の一般化である L (p; q)-ラベリング問題が q が p の約数でないすべての (p; q) の組に対し NP 困難であることと対照的である．A (p,q)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set of nonnegative integers such that |f(x)-f(y)| ≧ p if x is a vertex and y is an edge incident to x, and |f(x)-f(y)| ≧ q if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). A k-(p,q)-total labeling is a (p,q)-total labeling f:V(G) ∪ E(G) → {0,...,k}, and the (p,q)-total labeling problem asks the minimum k, which we denote by λTp,q(G), among all possible assignments. In this paper, we first give new upper and lower bounds on λTp,q(G) for some classes of graphs G, in particular, tight bounds on λTp,q(T) for trees T. We then show that if p ≦ 3q/2, the problem for trees T is linearly solvable, and give a complete characterization of trees achieving λTp,q(T) if in addition Δ ≧ 4 holds, where Δ is the maximum degree of T. It is contrasting to the fact that the L(p,q)-labeling problem, which is a generalization of the (p,q)-total labeling problem, is NP-hard for any two positive integers p and q such that q is not a divisor of p. 情報処理学会研究報告アルゴリズム(AL) 1884-0930 2010 2 1 8 20101112 read0191077/misc/37912056 HASUNUMA Toru 蓮沼徹 ISHII Toshimasa 石井利昌 ONO Hirotaka 小野廣隆 UNO Yushi 宇野裕之 A tight upper bound on the (2,1)-total labeling number of outerplanar graphs 外平面的グラフの(2,1)-全ラベリング数のタイトな上界 A (2,1)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set {0,1,...,k} of nonnegative integers such that |f(x)-f(y)|≧2 if x is a vertex and y is an edge incident to x, and |f(x)-f(y)|≧1 if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G)∪E(G). The (2,1)-total labeling number λ^T_2(G) of G is defined as the minimum k among all possible assignments. In [D. Chen and W. Wang. (2,1)-Total labelling of outerplanar graphs. Discr. Appl. Math. 155(2007)], it was conjectured that all outerplanar graphs G satisfy λ^T_2(G)≦Δ(G)+2, where Δ(G) is the maximum degree of G, while they also showed that it is true for G with Δ(G)≧5. In this paper, we solve their conjecture completely, by proving that λ^T_2(G)≦Δ(G)+2 even in the case of Δ(G)≦4. グラフGの(2,1)-全ラべリングとは,Gの節点と辺への0からkまでの整数値の割り当てであり,節点とそれに接続する辺の間では少なくとも2,隣り合う2節点間または2辺間では少なくとも1の差があるもののことをいう.Gの(2,1)-全ラべリング数λ^T_2(G)は,kがとりうる値の最小値として定義される. [D. Chen and W. Wang. (2,1)-Total labelling of outerplanar graphs. Discr. Appl. Math. 155(2007)]では,すべての外平面的グラフGにおいてλ^T_2(G)≦Δ(G)+2が成り立つと予想され(ただし,Δ(G)はGの最大次数を表す), Δ(G)≧5の場合この予想は成立することも証明されている.本研究では,Δ(G)≦4の場合においてもこの予想が成立することを示す. The Institute of Electronics, Information and Communication Engineers 一般社団法人電子情報通信学会 IEICE technical report 電子情報通信学会技術研究報告. COMP, コンピュテーション 0913-5685 110 12 1 8 20100415 read0191077/misc/37614801 HASUNUMA TORU 蓮沼徹 ISHII TOSHIMASA 石井利昌 ONO HIROTAKA 小野廣隆 UNO YUSHI 宇野裕之 A linear time algorithm for L(2, 1)-labeling of trees 木のL(2, 1)-ラベリングに対する線形時間アルゴリズムグラフの k-L(2, 1) -ラベリングとは，頂点への 0 から k までの整数値の割り当てであり，隣接頂点間では少なくとも 2，距離 2 の頂点間では少なくとも 1 の差があるもののことを言う．L(2, 1) -ラベリング問題とは，グラフに対する k-L(2, 1) ラベリングの中で最小の k を求めるものである．この問題は，木幅が 2 のグラフに対してでも NP 困難であることが知られている．一方，多項式時間アルゴリズムは，路や閉路，木といった限られたクラスにしか知られておらず，木に対するアルゴリズムの計算量も 10 年以上 O(Δ4.5n) 時間であった (ただし，Δ はグラフの最大次数，n は木の頂点数)．この計算量は最近になって O(min{n1.75, Δ1.5n}) 時間へと改善されたが，線形時間で解けるかどうかは未解決であった．本論文では，これを解決する木の L(2, 1) -ラベリングに対する線形時間アルゴリズムを提案する．An L(2, 1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that |f (x)- f (y)| ≥ 2 if x and y are adjacent and |f (x)- f (y)| ≥ 1 if x and y are at distance 2, for all x and y in V(G). A k-L(2, 1)-labeling is an L(2, 1)-labeling f : V(G) → {0, . . . , k}, and the L(2, 1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2, and tree is one of very few classes for which the problem is polynomially solvable. The running time of the best known algorithm for trees had been O(Δ4.5n) for more than a decade, and an O(min{n1.75, Δ1.5n})-time algorithm has appeared recently, where Δ is the maximum degree of T and n = |V(T)|, however, it has been open if it is solvable in linear time. In this paper, we finally settle this problem for L(2, 1)-labeling of trees by establishing a linear time algorithm. 情報処理学会研究報告アルゴリズム(AL) 0919-6072 2009 7 1 8 20091120 read0191077/misc/26502784 蓮沼徹石井利昌小野廣隆宇野裕之 2-F-11 An O(n log^2 n)-Time Algorithm for L(2,1)-Labeling of Trees 社団法人日本オペレーションズ・リサーチ学会日本オペレーションズ・リサーチ学会秋季研究発表会アブストラクト集 2008 308 309 20080910 read0191077/misc/37728547 Hasunuma Toru 蓮沼徹 Ishii Toshimasa 石井利昌 Ono Hirotaka 小野廣隆 Uno Yushi 宇野裕之 RA-002 An O(n log^2 n) Algorithm for L(2,1)-labeling of Trees RA-002 木のL(2,1)-ラベリングのためのO(n log^2 n)時間アルゴリズム(モデル・アルゴリズム・プログラミング,査読付き論文) Forum on Information Technology FIT(電子情報通信学会・情報処理学会)運営委員会情報科学技術フォーラム講演論文集 7 1 5 6 20080820 read0191077/misc/39221312 HASUNUMA Toru 蓮沼徹 ISHII Toshimasa 石井利昌 ONO Hirotaka 小野廣隆 UNO Yushi 宇野裕之 An O(n^<1.75>) Algorithm for L(2, 1)-labeling of Trees 木のL(2, 1)-ラベリングに対するO(n^<1.75>) 時間アルゴリズム An L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G)to the set of nonnegative integers such that |f(x)-f(y)|≧2 if x and y are adjacent and |f(x)-f(y)|≧1 if x and y are at distance 2 for all x and y in V(G). A k-L(2,1)-labeling is an assignment f:V(G)→{0,...,k}, and the L(2,1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2. Tree is one of a few classes for which the problem is polynomially solvable, but still only an O(Δ^<4.5>n) time algorithm for a tree T has been known so far, where Δ is the maximum degree of T and n=|V(T)|. In this paper, we first show that an existent necessary condition for λ(T)=Δ+1 is also sufficient for a tree T with Δ=Ω(√<n>), which leads to a linear time algorithm for computing λ(T) undeo this condition. We then show that λ(T) can be computed in O(Δ^<1.5>n) time for any tree T. Combining these, we finally obtain an O(n^<1.75>) time algorithm, which greatly improves the currently best known result. グラフのL(2,1)-ラベリングとは,頂点集合V(G)から非負整数への割当てfで,V(G)上のすべての隣接するxとyに対し,|f(x)-f(y)|≧2を満たし,すべての距離2で離れるxとyに対し,|f(x)-f(y)|≧1を満たすもののことを言う.k-L(2,1)-ラベリングとは,f:V(G)→{0,...,k}なる割当てfであり,L(2,1)-ラベリング問題とは,そのような最小のkを求める問題のことを言い,その最小値をλ(G)で表す.この問題はグラフの木幅が2のときでもNP困難であることが知られている.木はこの問題に対して多項式時間で求解可能な数少ないグラフクラスであるが,その計算量は小さくなく,最大次数Δ,頂点数nの木Tに対し,これまでO(Δ^<4.5>n)時間アルゴリズムしか知られていなかった.本論文では,まずλ(T)=Δ+1成立の既存の必要条件がΔ=Ω(√<n>)である木においては必要条件でもあることを示す.これによりΔ=Ω(√<n>)の場合にL(2,1)-ラベリングを求める線形時間アルゴリズムが得られる.次にλ(T)が任意の木に対してO(Δ^<1.5>n)時間で計算できることを示す.これらを組み合わせることにより,これまで知られていた最善の計算時間O(Δ^<4.5>n)を大幅に改善するO(n^<1.75>)時間アルゴリズムを提案する. The Institute of Electronics, Information and Communication Engineers 一般社団法人電子情報通信学会 IEICE technical report 電子情報通信学会技術研究報告. COMP, コンピュテーション 0913-5685 108 29 43 50 20080513 read0191077/misc/24050645 HASUNUMA Toru 蓮沼徹 Finding completely independent spanning trees in maximal planar graphs 極大平面グラフにおける完全独立全域木について Let G be a graph. Let T_1, T_2, ⋯, T_k be spanning trees in G. If for any two vertices u, v in G, the paths from u to v in T_i, i=1, 2, ⋯, k, are pairwise openly vertex-disjoint(i.e., edge-disjoint and internally vertex-disjoint), then we say that T_1, T_2, ⋯, T_k are completely independent. In this paper, we show that there are two completely independent spanning trees in a maximal planar graph G with at least 4 vertices if G has the property that there is no vertex inside a triangle(except for the outer triangle). Besides, we show that given a graph G, the problem of finding two completely independent spanning trees in G is NP-hard. T_1, T_2, ⋯, T_kをグラフGの全域木とする．Gの任意の二頂点u, vに対して，T_1, T_2, ⋯, T_kにおけるuからvへのパスが互いに辺素かつ内素であるときに，T_1, T_2, ⋯, T_kは完全独立であるという．本論文では，(外三角を除く)三角形内部に頂点を持たない，頂点数4以上の極大平面グラフには，2つの完全独立全域木が存在することを証明する．また, 与えられたグラフにおける2つの完全独立全域木を見つける問題はNP困難であることも証明する． The Institute of Electronics, Information and Communication Engineers 一般社団法人電子情報通信学会 IEICE technical report. Theoretical foundations of Computing 電子情報通信学会技術研究報告. COMP, コンピュテーション 0913-5685 100 568 55 62 20010100 read0191077/misc/38196707 NAGAMOCHI Hiroshi 永持仁 HASUNUMA Toru 蓮沼徹 An Efficient NC Algorithm for a Sparse k-Edge-Connectivity Certificate k-辺連結性を保存する疎なグラフを求める効率の良いNCアルゴリズム We present an efficient NC algorithm for finding a sparse k-edge-connectivity certificate of a multi-graph G. Our algorithm runs in O((logkn)(logk)^2(logn)^2)) time using O(k(n+m')) processors on a CRCW(ARBITRARY)PRAM, where n and m' stand for the numbers of vertices in G and edges in the simplified graph of G, respectively. 多重グラフGのk-辺連結性を保持する疎な全域部分多重グラフを，CRCW(ARBITRARY)PRAM上でO(k(n+m'))個のプロセッサを使用し，O((logkn)(logk)^2(logn)^2))時間で計算するNCアルゴリズムを与える．ここで，nはGの頂点数，m'はGを単純化して得られるグラフの辺の数を表す． The Institute of Electronics, Information and Communication Engineers 一般社団法人電子情報通信学会 IEICE technical report. Theoretical foundations of Computing 電子情報通信学会技術研究報告. COMP, コンピュテーション 98 137 39 46 19980623 read0191077/misc/38583504 HASUNUMA Toru 蓮沼徹 NAGAMOCHI Hiroshi 永持仁 Independent spanning trees with small depths in iterated line digraphs 反復ラインダイグラフの深さの浅い独立全域木 We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths. ダイグラフ(有向グラフ)の独立全域木に関する予想が，ダイグラフのクラスをラインダイグラフに限定した場合には成り立つことを証明する．又，反復ラインダイグラフの深さの浅い独立全域本を構成する．この結果から，de Brujn ダイグラフ及び Kautz ダイグラフの深さの浅い独立全域木が得られる．We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths. Information Processing Society of Japan (IPSJ) 一般社団法人情報処理学会 IPSJ SIG Notes 情報処理学会研究報告アルゴリズム(AL) 0919-6072 1997 92 17 24 19970919