Discussiones Mathematicae Graph Theory 27(1) (2007) 193-204
doi: 10.7151/dmgt.1355

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MORE ON EVEN [a,b]-FACTORS IN GRAPHS

Abdollah Khodkar  and  Rui Xu

Department of Mathematics
University of West Georgia
Carrollton, GA 30118, USA

Abstract

In this note we give a characterization of the complete bipartite graphs which have an even (odd) [a,b]-factor. For general graphs we prove that an a-edge connected graph G with n vertices and with δ(G) ≥ max{a+1,[an/(a+b)]+a−2} has an even [a,b]-factor, where a and b are even and 2 ≤ a ≤ b. With regard to the edge-connectivity this result is slightly better than one of the similar results obtained by Kouider and Vestergaard in 2004 and unlike their results, this result has no restriction on the order of graphs.

Keywords: [a,b]-factor; spanning graph; edge-connectivity.

2000 Mathematics Subject Classification: 05C40.

References

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[2] M. Kouider and P.D. Vestergaard, On even [2,b]-factors in graphs, Australasian J. Combin. 27 (2003) 139-147.
[3] M. Kouider and P.D. Vestergaard, Even [a,b]-factors in graphs, Discuss. Math. Graph Theory 24 (2004) 431-441, doi: 10.7151/dmgt.1242.
[4] M. Kouider and P.D. Vestergaard, Connected factors in graphs - a survey, Graphs and Combin. 21 (2005) 1-26, doi: 10.1007/s00373-004-0587-7.
[5] L. Lovász, Subgraphs with prescribed valencies, J. Combin. Theory 8 (1970) 391-416, doi: 10.1016/S0021-9800(70)80033-3.
[6] D.B. West, Introduction to Graph Theory (Prentice-Hall, Inc, 2000).

Received 17 March 2006
Revised 27 July 2006