On the Erdős-Sós Conjecture and maximum paths
نویسندگان
چکیده
Suppose G is a graph with average degree greater than k − 2. Erdős and Gallai proved that G contains a path on k vertices. In 1962, Erdős and Sós conjectured that G contains every tree on k vertices. Zhou proved the ErdősSós conjecture holds for the case where G has exactly k vertices. Wozniak proved the case where G has order k + 2. This paper’s authors proved the case where G has order k + 3 (as well as k + 1). We will prove the Erdős-Sós conjecture holds if a maximum path in G contains at most k + 3 vertices (no restriction is imposed on the order of G).
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