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                * Princeton Discrete Math Seminar *
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Speaker: Leo Versteegen (LSE)

Thursday 14th November, 3:00 in Fine Hall 224.

Title: Embedding trees in graphs with large minimum degree

In this talk, which is based on joint work with Alexey Pokrovskiy
and Ella Williams, we discuss the following variant of the Erdős-Sós
conjecture due to Besomi, Pavez-Signé, and Stein. If c is larger than 1/2,
and a graph G has minimum degree at least ck and maximum degree at least
4-4c, then every tree with k edges can be embedded into G. We prove an
approximate version of this conjecture for trees of bounded degree. The key
ingredient of the proof is a new structural lemma about graphs that do not
admit embeddings for all bounded degree trees.

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