Cliques in graphs with bounded minimum degree
نویسندگان
چکیده
منابع مشابه
Cliques in Graphs With Bounded Minimum Degree
Let fr(n, e) be the minimum number of r-cliques in graphs of order n and size e. Determining fr(n, e) has been a long-studied problem. The case r = 3, that is, counting triangles, has been studied by various people. Erdős [3], Lovász and Simonovits [7] studied the case when e = ( n 2 ) /2 + l with 0 < l n/2. Fisher [4] considered the situation when ( n 2 ) /2 e 2 ( n 2 ) /3, but it was not unti...
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For a graph G and a fixed integer k ≥ 3, let νk(G) denote the maximum number of pairwise edge-disjoint copies of Kk in G. For a constant c, let η(k, c) be the infimum over all constants γ such that any graph G of order n and minimum degree at least cn has νk(G) ≥ γn2(1 − on(1)). By Turán’s Theorem, η(k, c) = 0 if c ≤ 1− 1/(k− 1) and by Wilson’s Theorem, η(k, c) → 1/(k2 − k) as c → 1. We prove t...
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A graph G is called C4-free if it does not contain the cycle C4 as an induced subgraph. Hubenko, Solymosi and the first author proved (answering a question of Erdős) a peculiar property of C4-free graphs: C4 graphs with n vertices and average degree at least cn contain a complete subgraph (clique) of size at least c′n (with c′ = 0.1c2n). We prove here better bounds (c2n/3 in general and (c− 1/3...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2009
ISSN: 1571-0653
DOI: 10.1016/j.endm.2009.07.027