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Complete subgraphs of random graphs
, 2002
"... A classical theorem by Erdős, Kleitman and Rothschild on the structure of trianglefree graphs states that with high probability such graphs are bipartite. Our first main result refines this theorem by investigating the structure of the ’few ’ trianglefree graphs which are not bipartite. We prove t ..."
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Cited by 10 (3 self)
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that a fixed subgraph H occurs with extremely high probability in sufficiently dense εregular graphs. We prove this conjecture for the
Complete subgraphs in multipartite graphs
"... Turán’s Theorem states that every graphG of edge density ‖G‖/(G2)> k−2k−1 contains a complete graph Kk and describes the unique extremal graphs. We give a similar Theorem for `partite graphs. For large `, we find the minimal edge density dk ` , such that every `partite graph whose parts have ..."
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Cited by 2 (1 self)
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Turán’s Theorem states that every graphG of edge density ‖G‖/(G2)> k−2k−1 contains a complete graph Kk and describes the unique extremal graphs. We give a similar Theorem for `partite graphs. For large `, we find the minimal edge density dk ` , such that every `partite graph whose parts
On Vertexdisjoint Complete Subgraphs of a Graph
"... We conjecture that if G is a graph of order sk, where s ~3 and k 2: 1 are integers, and d(x)+d(y) ~ 2(s1)k for every pair of nonadjacent vertices x and y of G, then G contains k vertexdisjoint complete subgraphs of order s. This is true when s = 3, [6]. Here we prove this conjecture for k ~ 6. 1 ..."
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We conjecture that if G is a graph of order sk, where s ~3 and k 2: 1 are integers, and d(x)+d(y) ~ 2(s1)k for every pair of nonadjacent vertices x and y of G, then G contains k vertexdisjoint complete subgraphs of order s. This is true when s = 3, [6]. Here we prove this conjecture for k ~ 6
The Existence of Exactly mcoloured Complete Subgraphs
, 1996
"... this paper we will describe our main new method for constructing counterexamples. This will enable us to prove the following result. ..."
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Cited by 3 (0 self)
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this paper we will describe our main new method for constructing counterexamples. This will enable us to prove the following result.
Note On the Number of Complete Subgraphs Contained in Certain Graphs
, 1981
"... We count the number of complete graphs of order 4 contained in certain graphs. ..."
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We count the number of complete graphs of order 4 contained in certain graphs.
ON THE NUMBER OF COMPLETE SUBGRAPHS AND CIRCUITS CONTAINED IN GRAPHS
, 1968
"... Dedicated to V. JARNiK on the occasion of his 70th birthday. Denote by W(n; k) a graph of n vertices and k edges. Put for n r (mod p 1) m(n,p) = p2 (n 2r 2)+ ( r), 0<_n_<p1 2(p 1) 22 and denote by K P the complete graph of p vertices. A well known theorem of TUR.áN [6] states that every ..."
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Dedicated to V. JARNiK on the occasion of his 70th birthday. Denote by W(n; k) a graph of n vertices and k edges. Put for n r (mod p 1) m(n,p) = p2 (n 2r 2)+ ( r), 0<_n_<p1 2(p 1) 22 and denote by K P the complete graph of p vertices. A well known theorem of TUR.áN [6] states
12 On Induced Subgraphs of Finite Graphs not Containing Large Empty and Complete Subgraphs
, 2014
"... ar ..."
Ramsey problem on Multiplicities of Complete Subgraphs in Nearly Quasirandom Graphs.
"... Let kt(G) be the number of cliques of order t in the graph G. For a graph G with n vertices let ct(G) = kt(G)+kt ( ¯ G) ( n. Let ct(n) = t) Min{ct(G) : G  = n} and let ct = limn→ ∞ ct(n). An old conjecture of Erdös [2] related to Ramsey’s theorem states that ct = 2 1−(t 2). Recently it was show ..."
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Cited by 3 (1 self)
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Let kt(G) be the number of cliques of order t in the graph G. For a graph G with n vertices let ct(G) = kt(G)+kt ( ¯ G) ( n. Let ct(n) = t) Min{ct(G) : G  = n} and let ct = limn→ ∞ ct(n). An old conjecture of Erdös [2] related to Ramsey’s theorem states that ct = 2 1−(t 2). Recently it was shown to be false by A. Thomason [12]. It is known that ct(G) ∼ 2 1−(t 2) whenever G is a pseudorandom graph. Pseudorandom graphs the graphs ”which behave like random graphs ”were introduced and studied in [1] and [13]. The aim of this paper is to show that for t = 4, ct(G) ≥ 2 1−(t 2) if G is a graph arising from pseudorandom by a small perturbation. 1 Introduction. Denote by kt(G) the number of cliques of order t in the graph G. For a graph
Results 1  10
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