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Complementary Cycles in Regular Multipartite Tournaments, Where One Cycle Has Length Four

Lutz Volkmann
경북대학교 자연과학대학 수학과|2004.06|Kyungpook Mathematical Journal|제44권 제2호|pp. 219-247

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Abstract

The vertex set of a digraph D is denoted by V(D). A c-partite tournament is an orientation of a complete c-partite graph.In 1999, Yeo conjectured that each regular c-partite tournament D with c 4 and jV(D)j 8 contains a pair of vertex disjoint directed cycles of lengths 4 and jV(D)j 4. An example will demonstrate that Yeo’s conjecture is not true in general for regular 4-partite tournaments with two vertices in each partite. However, in all other cases we shall confirm this conjecture in affirmative.

참고문헌 (13)

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  2. Y. Guo, "Habilitation Thesis", pp.102~ (1998), RWTH Aachen
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  4. "On subtournaments of a tournament", 9, pp.297~301 (1966)
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  6. "Complementary cycles of all lengths in tournaments", 57, pp.18~25 (1993)
  7. "Strong subtournaments of multipartite tournaments", 20, pp.189~196 (1999)
  8. "Cycles in multipartite tournaments: results and problems", pp.19~53 (2002), Discrete Math.
  9. "Complementary cycles in regular multipartite tournaments" (2002)
  10. "Almost regular multipartite tournaments containing a Hamiltonian path through a given arc" (2002)
  11. "One-diregular subgraphs in semicomplete multipartite digraphs", 24, pp.175~185 (1997)
  12. "Diregular c-partite tournaments are vertex-pancyclic when c ¸ 5", 32, pp.137~152 (1999)
  13. "How close to regular must a semicomplete multipartite digraph be to secure Hamiltonicity?", 15, pp.481~493 (1999)

관련 논문AI추천

Cycles through a given set of vertices in regular multipartite tournamentsLutz Volkmann, Stefan Winzen대한수학회 · 대한수학회지2007 · 제44권 제3호Weakly Complementary Cycles in 3-Connected Multipartite TournamentsLutz Volkmann, Stefan Winzen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제2호Locally semicomplete digraphs with a factor composed of $k$cyclesRonald J. Gould, Yubao Guo대한수학회 · 대한수학회지2004 · 제41권 제5호Circulant Decompositions of Certain Multipartite Graphs into Gregarious Cycles of a Given Length조정래영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호A note on decomposition of complete equipartite graphs into gregarious $6$-cycles조정래대한수학회 · 대한수학회보2007 · 제44권 제4호PANCYCLIC ARCS IN HAMILTONIAN CYCLES OF HYPERTOURNAMENTSMichel Surmacs, Yubao Guo대한수학회 · 대한수학회지2014 · 제51권 제6호

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