A minimum degree condition of fractional (k, m)-deleted graphs

Let G be a graph of order n, and let k >= 1 and m >= 1 be two integers. In this paper, we consider the relationship between the minimum degree delta(G) and the fractional (k, m)-deleted graphs. It is proved that if n >= 4k - 5 + 2(2k + 1)m and delta(G) >= n/2, then G is a fractional (k, m)-deleted graph. Furthermore, we show that the minimum degree condition is sharp in some sense. To cite this article: S. Zhou, C R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.