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

Affiliation(s)

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

Department of Aerial Ammunition, Air Force Logistic College, Xuzhou, China.

Department of Fundamental Courses, Air Force Logistic College, Xuzhou, China.

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

Department of Aerial Ammunition, Air Force Logistic College, Xuzhou, China.

Department of Fundamental Courses, Air Force Logistic College, Xuzhou, China.

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, .

Cite this paper

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.

J. Lei, Q. Yu, C. Huang and M. Liu, "A Neighborhood Condition for Graphs to Have Special [a,b]-Factor,"

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

[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