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

1.

References

1.

J. Bang-Jensen, Locally semicomplete digraphs: A generalization of tournaments, J. Graph Theory 14 (1990), 371–390.

2.

J. Bang-Jensen, Y. Guo, G. Gutin and L. Volkmann, A classification of locally semicomplete digraphs, Discrete Math. 167/168 (1997), 101–114.

3.

G.-T. Chen, R. J. Gould and H. Li, Partitioning Vertices of a Tournament into Independent Cycles, J. Combin. Theory Ser. B 83 (2001), 213–220

4.

Y. Guo, Locally Semicomplete Digraphs. PhD thesis, RWTH Aachen, Germany. Aachener Beitrage zur Mathematik, Band 13, Augustinus-Buchhandlung achen, 1995

5.

Y. Guo and L. Volkmann, On complementary cycles in locally semicomplete digraphs, Discrete Math. 135 (1994), 121–127

6.

Y. Guo and L. Volkmann, Locally semicomplete digraphs that are complementary m-pancyclic, J. Graph Theory 21 (1996), 121–136