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

  • Zhou, Sizhong (SCHOOL OF MATHEMATICS AND PHYSICS JIANGSU UNIVERSITY OF SCIENCE AND TECHNOLOGY)
  • Published : 2008.02.29

Abstract

Let G be a graph, and let a, b, k be integers with $0{\leq}a{\leq}b,k\geq0$. 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

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 https://doi.org/10.1007/s003730050035
  3. H. Enomoto and M. Hagita, Toughness and the existence of k-factors. IV, Discrete Math. 216 (2000), no. 1-3, 111-120 https://doi.org/10.1016/S0012-365X(99)00298-8
  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 https://doi.org/10.1007/s003730050053
  6. D. R. Woodall, The binding number of a graph and its Anderson number, J. Combinatorial Theory Ser. B 15 (1973), 225-255 https://doi.org/10.1016/0095-8956(73)90038-5
  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

Cited by

  1. A sufficient condition for a graph to be an (a, b, k)-critical graph vol.87, pp.10, 2010, https://doi.org/10.1080/00207160902777914