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The Erdős-Sós conjecture for graphs of girth 5

FB Mathematik, Freie Universität Berlin, Graduiertenkolleg ‘Alg. Diskr. Mathematik’, Arnimallee 2–6, 14195 Berlin, Germany; Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA
Discrete Mathematics (Impact Factor: 0.58). 01/1996; DOI: 10.1016/0012-365X(95)00207-D

ABSTRACT We prove that every graph of girth at least 5 with minimum degree δ ⩾ k/2 contains every tree with k edges, whose maximum degree does not exceed the maximum degree of the graph. An immediate consequence is that the famous Erdős-Sós Conjecture, saying that every graph of order n with more than n(k − 1)/2 edges contains every tree with k edges, is true for graphs of girth at least 5.

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