Title

On the Erdos-Sós conjecture for graphs having no path with k + 4 vertices

Document Type

Article

Date of Original Version

1-1-2013

Abstract

When G is a graph with average degree greater than k - 2, Erdos and Gallai proved that G contains a path on k vertices. Erdos and Sós conjectured that under the same condition, G should contain every tree on k vertices. Several results based upon the number of vertices in G have been proved including the special cases where G has exactly k vertices (Zhou), k + 1 vertices (Slater, Teo and Yap), k + 2 vertices (Woźniak) and k + 3 vertices (Tiner). To strengthen these results, we will prove that the Erdos-Sós conjecture holds when the graph G contains no path with k + 4 vertices (no restriction is imposed on the number of vertices of G). © 2013 Elsevier B.V. All rights reserved.

Publication Title

Discrete Mathematics

Volume

313

Issue

16

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