LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES

- Journal title : Journal of the Korean Mathematical Society
- Volume 41, Issue 5, 2004, pp.895-912
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2004.41.5.895

Title & Authors

LOCALLY SEMICOMPLETE DIGRAPHS WITH A FACTOR COMPOSED OF k CYCLES

Gould, Ronald J.; Guo, Yubao;

Gould, Ronald J.; Guo, Yubao;

Abstract

A digraph is locally semicomplete if for every vertex , the set of in-neighbors as well as the set of out-neighbors of 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.

Keywords

cycle;factor;strong connectivity;locally semicomplete digraph;

Language

English

Cited by

2.

References

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