A Neighborhood Condition for Graphs to Have Special [a,b]-Factor

Jinguo Lei, Qingzhi Yu, Changhua Huang, Man Liu

Department of Aerial Ammunition, Air Force Logistic College, Xuzhou, China.
Department of Aerial Four Station Support, Xuzhou Air Force Logistic College, Xuzhou, China.
Department of Fundamental Courses, Air Force Logistic College, Xuzhou, China.

DOI: 10.4236/am.2014.51022                

Abstract

Let G be a graph of order n, and let a and b be integers, such that 1 ≤ a < b. Let H be a subgraph of G with m(≤b) edges, and δ(G) be the minimum degree. We prove that G has a [a,b]-factor containing all edges of H if , , and when a ≤ 2, .

Keywords

Graph; Factor; [a, b]-Factor; The Minimum Degree; Neighborhood Condition

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” American Elsevier, New York, 1976.
[2]	Y. Egawa and H. Enomoto, “Sufficient Conditions for the Existence of k-Factors,” Recent Studies in Graph Theory, Vishwa International Publications, India, 1989, pp. 96-105.
[3]	P. Katerinis, “Minimum Degree of a Graph and the Existence of k-Factors,” Proceedings of the Indian Academy of Sciences, Vol. 94, No. 2, 1985, pp. 123-127.
[4]	T. Iida and T. Nishimura, “An Ore-Type Conditions for the Existence of k-Factors in Graphs,” Graphs and Combinatorics, Vol. 7, No. 4, 1991, pp. 353-361. http://dx.doi.org/10.1007/BF01787640
[5]	H. Y. Pan, “[a,b]-Facor of Graph G,” Master Paper, Shandong University, Jinan, 1996.
[6]	G. Li and G. Liu, “(g,f)—Factorizations Orthogonal to a Subgraph in Graphs,” Science in China (A), Vol. 41, No. 3, 1998, pp. 267-272. http://dx.doi.org/10.1007/BF02879045