A Variation of a Conjecture Due to Erds and Sós

Erdos and Sos conjectured in 1963 that every graph G on n vertices with edge numbere(G) > 1/2(k - 1)n contains every tree T with k edges as a subgraph.In this paper,we consider avariation of the above conjecture,that is,for n > 9/2k~2 + 37/2k + 14 and every graph G on n vertices withe(G) > 1/2 (k-1)n,we prove that there exists a graph G’ on n vertices having the same degree sequenceas G and containing every tree T with k edges as a subgraph.