SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 52, Issue 1, 2015, pp.287-299
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2015.52.1.287

Title & Authors

SUFFICIENT CONDITION FOR THE EXISTENCE OF THREE DISJOINT THETA GRAPHS

Gao, Yunshu; Ma, Ding;

Gao, Yunshu; Ma, Ding;

Abstract

A theta graph is the union of three internally disjoint paths that have the same two distinct end vertices. We show that every graph of order and size at least contains three disjoint theta graphs. As a corollary, every graph of order and size at least contains three disjoint cycles of even length.

Keywords

disjoint theta graphs;sufficient condition;minimum degree;

Language

English

References

1.

J. A. Bondy and U. S. R. Murty, Graph Theory, the second edition, Springer, 2008.

2.

S. Chiba, S. Fujita, Y. Gao, and G. Li, On a sharp degree sum condition for disjoint chorded cycles in graphs, Graphs Combin. 26 (2010), no. 2, 173-186.

3.

K. Corradi and A. Hajnal, On the maximal number of independent circuits in a graph, Acta Math. Acad. Sci. Hungar. 14 (1963), 423-439.

4.

G. A. Dirac, On the maximal number of independent triangles, Abh. Math. Sem. Univ. Hamburg 26 (1963), 78-82.

5.

H. Enomoto, On the existence of disjoint cycles in a graph, Combinatorica 18 (1998), no. 4, 487-492.

6.

D. Finkel, On the number Of independent chorded cycle in a graph, Discrete Math. 308 (2008), no. 22, 5265-5268.

7.

Y. Gao and N. Ji, The extremal function for two disjoint cycles, Bull. Malays. Math. Sci. Soc. DOI:10.1007/s40840-014-0102-0,2014.

9.

L. Posa, On the circuits of finite graphs, Magyar Tud. Akad. Mat. Kut. Int. Kozl. 8 (1963), 355-361.