Geodesic
More on even [a,b]-factors in graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 193-204

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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) ≥ maxa+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 
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Khodkar, Abdollah; Xu, Rui. More on even [a,b]-factors in graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 193-204. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a16/