Degree Conditions for Graphs to Be Fractional k-Covered Graphs

摘要

Let k >= 3 be an integer, and let G be a graph of order n with n >= max{10, 4k - 3}, and delta(G) >= k+1. If G satisfies max{d(G)(x), d(G)(y)} >= n+1/2 for each pair of nonadjacent vertices x, y of G, then G is a fractional k-covered graph. The result is best possible in some sense, and it is an improvement and extension of C. Wang and C. Ji's result (C. Wang and C. 31, Some new results on k-covered graphs, Mathematica Applicata 11(1)(1998), 61-64).