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Journal Articles Journal of Graph Theory Year : 2020

A variant of the Erdős‐Sós conjecture

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Abstract

A well-known conjecture of Erdős and Sós states that every graph with average degree exceeding $m−1$ contains every tree with m edges as a subgraph. We propose a variant of this conjecture, which states that every graph of maximum degree exceeding m and minimum degree at least $[\frac{2m}{3}]$ contains every tree with m edges. As evidence for our conjecture we show (i) for every m there is a g(m) such that the weakening of the conjecture obtained by replacing the first m by g(m) holds, and (ii) there is a $\gamma > 0$ such that the weakening of the conjecture obtained by replacing $[\frac{2m} {3}$ by $(1 − \gamma)m$ holds.
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Dates and versions

hal-02497401 , version 1 (03-03-2020)

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Frédéric Havet, Bruce Reed, Maya Stein, David R Wood. A variant of the Erdős‐Sós conjecture. Journal of Graph Theory, 2020, 94 (1), pp.131-158. ⟨10.1002/jgt.22511⟩. ⟨hal-02497401⟩
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