On the Erdös-Sós conjecture and graphs with large minimum degree

Authors

Nancy Eaton, University of Rhode Island
Gary Tiner, Faulkner University

Document Type

Article

Date of Original Version

4-1-2010

Abstract

Suppose G is a simple graph with average vertex degree greater than k - 2. Erdös and Sós conjectured that G contains every tree on k vertices. Sidorenko proved G contains every tree that has a vertex v with at least [k/2] -1 leaf neighbors. We prove this is true if v has only [k/2] - 2 leaf neighbors. We generalize Sidorenko's result by proving that if G has minimum degree d, then G contains every tree that has a vertex with least (k-1) - d leaf neighbors. We use these results to prove that if G has average degree greater than k - 2 and minimum degree at least k - 4, then G contains every tree on k vertices.

Publication Title, e.g., Journal

Ars Combinatoria

Volume

95

Citation/Publisher Attribution

Eaton, Nancy, and Gary Tiner. "On the Erdös-Sós conjecture and graphs with large minimum degree." Ars Combinatoria 95, (2010): 373-382. https://digitalcommons.uri.edu/math_facpubs/115