Small complete minors above the extremal edge density
نویسندگان
چکیده
منابع مشابه
Small Complete Minors Above the Extremal Edge Density
A fundamental result of Mader from 1972 asserts that a graph of high average degree contains a highly connected subgraph with roughly the same average degree. We prove a lemma showing that one can strengthen Mader’s result by replacing the notion of high connectivity by the notion of vertex expansion. Another well known result in graph theory states that for every integer t there is a smallest ...
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Let G and H be graphs. As usual, we say that H is a minor or subcontraction of G if V(G) contains disjoint subsets Wu , u # V(H), such that G[Wu] is connected for each u # V(H) and there is an edge in G between Wu and Wv whenever uv # E(H). (Here, G[Wu] stands for the subgraph of G induced by Wu ; our notation is standard and follows that of Bolloba s [2].) We write GoH if H is a minor of G, an...
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Let H be a graph. If G is an n-vertex simple graph that does not contain H as a minor, what is the maximum number of edges that G can have? This is at most linear in n, but the exact expression is known only for very few graphs H . For instance, when H is a complete graph Kt, the “natural” conjecture, (t− 2)n− 12(t− 1)(t− 2), is true only for t ≤ 7 and wildly false for large t, and this has rat...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2015
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-015-3013-2