Abstract:The graph removal lemma is a fundamental result in extremal graph theory which says that for every fixed graph H and ε > 0, if an n-vertex graph G contains εn 2 edge-disjoint copies of H then G contains δn v(H) copies of H for some δ = δ(ε, H) > 0. The current proofs of the removal lemma give only very weak bounds on δ(ε, H), and it is also known that δ(ε, H) is not polynomial in ε unless H is bipartite. Recently, Fox and Wigderson initiated the study of minimum degree conditions guaranteeing that δ(ε, H) depe… Show more
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