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

DOI: 10.4236/am.2014.51022   PDF   HTML     4,567 Downloads   5,662 Views  


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, .

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J. Lei, Q. Yu, C. Huang and M. Liu, "A Neighborhood Condition for Graphs to Have Special [a,b]-Factor," Applied Mathematics, Vol. 5 No. 1, 2014, pp. 212-215. doi: 10.4236/am.2014.51022.

Conflicts of Interest

The authors declare no conflicts of interest.


[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

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