LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES

Title & Authors
LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES
Gould, Ronald J.; Guo, Yubao;

Abstract
A digraph is locally semicomplete if for every vertex $\small{\chi}$, the set of in-neighbors as well as the set of out-neighbors of $\small{\chi}$ induce semicomplete digraphs. Let D be a k-connected locally semicomplete digraph with k $\small{\geq}$ 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.
Keywords
cycle;factor;strong connectivity;locally semicomplete digraph;
Language
English
Cited by
1.
Cycle factors in strongly connected local tournaments, Discrete Mathematics, 2010, 310, 4, 850
2.
Problems and conjectures concerning connectivity, paths, trees and cycles in tournament-like digraphs, Discrete Mathematics, 2009, 309, 18, 5655
3.
All 2-connected in-tournaments that are cycle complementary, Discrete Mathematics, 2008, 308, 11, 2115
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