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On embedding well-separable graphs. (English) Zbl 1157.05032
This paper is about guaranteeing that a given graph H is a subgraph of an arbitrary graph G. The author considers graphs H that are “far from being an expander”, namely H is well-separable if there is a subset SV(H) of size o(n) such that all components of H-S are of size o(n). Let Δ denote the maximum degree of H and χ its chromatic number. The author shows that if H is well-seperable, then for every Δ and γ>0 there exists an n 0 such that if G is of order nn 0 and minimum degree δ(G)(1-1/(2(χ-1))+γ)n, one gets HG. This work can be considered as a generalization of Turán’s Theorem, as well of a generalization of work by Erdös-Stone-Simonovits.
MSC:
05C35Extremal problems (graph theory)
05C10Topological graph theory
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