A variation of a conjecture due to Erdös and Sós.

Erdös and Sós conjectured in 1963 that every graph G on n vertices with edge number e( G) > ½ ( k − 1) n contains every tree T with k edges as a subgraph. In this paper, we consider a variation of the above conjecture, that is, for n ≥ 9/2 k² + 37/2 k+14 and every graph G on n vertices with e( G) > ½ ( k − 1) n, we prove that there exists a graph G′ on n vertices having the same degree sequence as G and containing every tree T with k edges as a subgraph. [ABSTRACT FROM AUTHOR]

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