Proof of the Loebl–Komlós–Sós conjecture for large, dense graphs |
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Authors: | Oliver Cooley |
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Institution: | aUniversity of Birmingham, United Kingdom |
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Abstract: | The Loebl–Komlós–Sós conjecture states that for any integers k and n, if a graph G on n vertices has at least n/2 vertices of degree at least k, then G contains as subgraphs all trees on k+1 vertices. We prove this conjecture in the case when k is linear in n, and n is sufficiently large. |
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Keywords: | Embedding Regularity lemma Loebl– Komló s– Só s conjecture Ramsey numbers of trees |
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