BINDING NUMBER CONDITIONS FOR (a, b, k)-CRITICAL GRAPHS

Title & Authors
BINDING NUMBER CONDITIONS FOR (a, b, k)-CRITICAL GRAPHS
Zhou, Sizhong;

Abstract
Let G be a graph, and let a, b, k be integers with $\small{0{\leq}a{\leq}b,k\geq0}$. Then graph G is called an (a, b, k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a, b]-factor. In this paper, the relationship between binding number bind(G) and (a, b, k)-critical graph is discussed, and a binding number condition for a graph to be (a, b, k)-critical is given.
Keywords
graph;[a, b]-factor;binding number;(a, b, k)-critical graph;
Language
English
Cited by
1.
A sufficient condition for a graph to be an (a, b, k)-critical graph, International Journal of Computer Mathematics, 2010, 87, 10, 2202
References
1.
J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, American Elsevier Publishing Co., Inc., New York, 1976

2.
M. Cai, O. Favaron, and H. Li, (2,k)-factor-critical graphs and toughness, Graphs Combin. 15 (1999), no. 2, 137-142

3.
H. Enomoto and M. Hagita, Toughness and the existence of k-factors. IV, Discrete Math. 216 (2000), no. 1-3, 111-120

4.
G. Liu and J. Wang, (a,b,k)-critical graphs, Adv. Math. (China) 27 (1998), no. 6, 536-540

5.
M. Shi, X. Yuan, M. Cai, and O. Favaron, (3,k)-factor-critical graphs and toughness, Graphs Combin. 15 (1999), no. 4, 463-471

6.
D. R. Woodall, The binding number of a graph and its Anderson number, J. Combinatorial Theory Ser. B 15 (1973), 225-255

7.
Q. Yu, Characterizations of various matching extensions in graphs, Australas. J. Combin. 7 (1993), 55-64

8.
S. Z. Zhou, Sufficient conditions for (a,b,k)-critical graphs, J. Jilin Univ. Sci. 43 (2005), no. 5, 607-609