Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES

  • Published : 2004.09.01
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Abstract

A digraph is locally semicomplete if for every vertex $\chi$, the set of in-neighbors as well as the set of out-neighbors of $\chi$ induce semicomplete digraphs. Let D be a k-connected locally semicomplete digraph with k $\geq$ 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.

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References

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Cited by

  1. Cycle factors in strongly connected local tournaments vol.310, pp.4, 2010, https://doi.org/10.1016/j.disc.2009.09.025
  2. Problems and conjectures concerning connectivity, paths, trees and cycles in tournament-like digraphs vol.309, pp.18, 2009, https://doi.org/10.1016/j.disc.2008.04.016
  3. All 2-connected in-tournaments that are cycle complementary vol.308, pp.11, 2008, https://doi.org/10.1016/j.disc.2006.12.008