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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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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
Book Ramsey Numbers I
, 2008
"... A book Bp is a graph consisting of p triangles sharing a common edge. In this paper we prove that if p ≤ q/6 − o (q) and q is large then the Ramsey number r (Bp, Bq) is given by r (Bp, Bq) = 2q + 3 and the constant 1/6 is essentially best possible. Our proof is based on Szemerédi’s uniformity lemma ..."
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A book Bp is a graph consisting of p triangles sharing a common edge. In this paper we prove that if p ≤ q/6 − o (q) and q is large then the Ramsey number r (Bp, Bq) is given by r (Bp, Bq) = 2q + 3 and the constant 1/6 is essentially best possible. Our proof is based on Szemerédi’s uniformity lemma and a stability result for books.