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Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) n 2 wi ..."
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Cited by 1802 (19 self)
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A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) n 2 with 0 < α < 17 −3 (), and G has no book of size at least graph G1 of order at least
Large generalized books are pgood
 J. Combin. Theory Ser. B
"... Let B (r) q = Kr + qK1 be the graph consisting of q distinct (r + 1)cliques sharing a common rclique. We prove that if p ≥ 2 and r ≥ 3 are fixed, then for all sufficiently large q. r(Kp+1,B (r) q) = p(q + r − 1) + 1 ..."
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Cited by 3 (3 self)
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Let B (r) q = Kr + qK1 be the graph consisting of q distinct (r + 1)cliques sharing a common rclique. We prove that if p ≥ 2 and r ≥ 3 are fixed, then for all sufficiently large q. r(Kp+1,B (r) q) = p(q + r − 1) + 1
Ramsey Numbers Involving Cycles
"... We gather and review general results and data on Ramsey numbers involving cycles. This survey is based on the author’s 2009 revision #12 of the Dynamic Survey DS1, "Small Ramsey Numbers", at the ..."
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We gather and review general results and data on Ramsey numbers involving cycles. This survey is based on the author’s 2009 revision #12 of the Dynamic Survey DS1, "Small Ramsey Numbers", at the