Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey

Gutin, Gregory

doi:10.1002/jgt.3190190405

Cited by 58 publications

(51 citation statements)

References 55 publications

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“…We point out here that Theorem 7.7 does not hold for semicomplete multipartite digraphs, as one can see from the examples in [19,56] (see, also, [55]). Very recently the authors and A. Yeo gave a polynomial algorithm for the hamiltonian cycle problem in semicomplete multipartite digraphs.…”

Section: Theorem 77 [14] An Extended Locally Semicomplete Digraph Imentioning

confidence: 88%

“…, m k . For k = 2 the value of this function was determined by Soltes (for details see [55]). For k ≥ 3 the function was investigated independently in [53,65,73].…”

Section: Problem 141mentioning

confidence: 99%

“…This characterization implies that the hamiltonian path problem is tractable for this important class of digraphs that remained for a long time the only generalization of tournaments (other than the semicomplete digraphs) to be studied. It was also known (see, e.g., [55]) that the hamiltonian cycle problem for semicomplete multipartite digraphs was quite difficult. A polynomial algorithm for this problem was recently found [22].…”

Section: Introductionmentioning

confidence: 98%

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Generalizations of tournaments: A survey

Bang‐Jensen¹,

Gutin

1998

J. Graph Theory

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We survey results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with a very rich structure. We describe, among numerous other topics mostly related to paths and cycles, results on hamiltonian paths and cycles. The reader will see that although these problems are polynomially solvable for all of the classes described, they can be highly non-trivial, even for these "tournament-like" digraphs.

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Section: Theorem 77 [14] An Extended Locally Semicomplete Digraph Imentioning

confidence: 88%

“…, m k . For k = 2 the value of this function was determined by Soltes (for details see [55]). For k ≥ 3 the function was investigated independently in [53,65,73].…”

Section: Problem 141mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Generalizations of tournaments: A survey

Bang‐Jensen¹,

Gutin

1998

J. Graph Theory

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“…There is extensive literature on cycles in multipartite tournaments, see e.g., BangJensen and Gutin [1], Guo [6], Gutin [7], Volkmann [13] and Yeo [17]. Many results are about the existence of cycles of a given length as e.g.…”

Section: )mentioning

confidence: 99%

Cycles with a given number of vertices from each partite set in regular multipartite tournaments

Volkmann

Winzen

2006

Czech Math J

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“…When k = 2, a multipartite tournament is called a bipartite tournament. Tournaments and multipartite tournaments are arguably the most studied digraph classes for dicycle problems (See, e.g., the surveys [51] and [11]). Since these graphs are relatively dense, many cycle properties may be expected to hold for these graphs.…”

Section: N} (Through Every Vertex V Of D) Then D Is Called Even (Vmentioning

confidence: 99%

Paths, Cycles and Related Partitioning Problems in Graphs

Zhang¹

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P a t h s , Cy c l e s a n d Re l a t e d P a r t i t i o n i n g P r o b l e ms i n Gr a p h s P a t h s , Cy c l e s a n d Re l a t e d P a r t i t i o n i n g P r o b l e ms i n Gr a p h s Paths, Cycles and Related Partitioning Problems in Graphs Zanbo ZhangThe research was supported by and carried out in the group of Formal Methods and Tools, in the Faculty of Electrical Engineering, Mathematics and Computer Science of the University of Twente, the Netherlands. The financial support from the University of Twente for this research work and its publication is gratefully acknowledged.The research was also supported by the National Natural Science Foundation of China (NSFC, 11471003 and 11471342) Copyright c⃝2017 Zanbo Zhang, Enschede, the Netherlands. All rights reserved. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission from the copyright owner. PATHS, CYCLES AND RELATED PARTITIONING PROBLEMS IN GRAPHS DISSERTATION PrefaceThis thesis is based on joint work of the author with several different collaborators during the last five years. It is composed of a short introductory chapter, followed by five technical chapters. These five chapters are all based on associated research papers that are in different stages of submission, refereeing, acceptance or publication, and that are listed below together with several other joint publications of the author.The underlying research papers as well as the corresponding chapters in this thesis are the result of continuous part-time research efforts of the author, in collaboration with other researchers, on paths and cycles in graphs.The first chapter contains a brief introduction, with some background and motivation for the research in this field, and with some remarks on earlier work that inspired the author to contribute to this field. The details of the author's contributions are presented in the subsequent five chapters, that are all self-contained. The second chapter deals with the extremal digraphs one has to exclude when relaxing a classical degree condition for the existence of Hamiltonian cycles in digraphs. The third and fourth chapter deal with sufficient conditions for path extendability and cycle extendability in digraphs, respectively. In the fifth chapter, in the context of path and cycle properties, we study the number of 2-paths in oriented graphs and tournaments. We also present some applications to demonstrate the relevance of conditions in terms of the number of 2-paths. In the sixth chapter, we study monochromatic clique and multicolored cycle partitioning problems in edge-colored graphs, from the perspective of computational complexity and algorithmic solutions. i ii PrefaceThe thesis has been written as a collection of independent papers. To guarantee the independence and readability of the chapters, we chose to maintain the structure of journal papers, with a short introduction and background, and th...

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Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey

Cited by 58 publications

References 55 publications

Generalizations of tournaments: A survey

Generalizations of tournaments: A survey

Cycles with a given number of vertices from each partite set in regular multipartite tournaments

Paths, Cycles and Related Partitioning Problems in Graphs

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