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Locally semicomplete digraphs with a factor composed of $k$cycles
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Abstract
A digraph is locally semicomplete if for every vertex x, the set of in-neighbors as well as the set of out-neighbors of x induce semicomplete digraphs. Let D be a k-connected locally semicomplete digraph with k ≥ 3 and g denote the length of a longest induced cycle of D. It is shown that if D has at least 7(k − 1)g vertices, then D has a factor composed of k cycles; furthermore, if D is semicomplete and with at least 5k + 1 vertices, then D has a factor composed of k cycles and one of the cycles is of length at most 5. Our results generalize those of [3] for tournaments to locally semicomplete digraphs.
참고문헌 (9)
- J. Bang-Jensen, "A generalization of tournaments" (1990)
- "A classication of locallysemicomplete digraphs", pp.101~114 (1997)
- "Partitioning Vertices of a Tournament intoIndependent Cycles", 83, pp.213~220 (2001)
- "PhD thesis, RWTH Aachen, Germany.Aachener Beitr？" (1995), Augustinus-Buchhandlung Aachen
- "On complementary cycles in localy semicomplete di-graphs" (1994)
- "Localy semicomplete digraphs that are complementarym-pancyclic", 21, pp.121~136 (1996)
- "On subtournaments of a tournament", 9, pp.297~301 (1996)
- "Two complementary circuits in two-connected tournaments" (1985)
- "Complementary cycles of all lengths in tournaments"
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