On book-complete graph Ramsey numbers
type: Item
instance of: scholarly article
title: On book-complete graph Ramsey numbers
zbMATH Open document ID: 0861.05046
author: Yusheng Li
author: Cecil Rousseau
published in: Journal of Combinatorial Theory. Series B
publication date: 1996-10-14T00:00:00Z
review text: The book \(B_k\) is the graph consisting of \(m\) triangles sharing one edge. It has been conjectured that the book-complete graph Ramsey number satisfies \(r(B_m,K_n)=(m+1)(n-1)+1\) for a fixed \(n\) and sufficiently large \(m\). The authors prove that for all \(m\geq 1\) and \(n\geq 3\) the inequalities \[ r(B_m,K_n)\leq{mn^2\over\log(n/e)}\quad\text{and}\quad r(K_1+T_m,K_n)\leq{(2m-1)n^2\over\log(n/e)} \] are satisfied. In the last inequality, \(T_m\) is any tree with \(m\) edges. For fixed \(m\), these bounds are asymptotically the best.
reviewed by: Ľubomír Šoltés
Mathematics Subject Classification ID: 05C55
zbMATH DE Number: 934823
zbMATH Keywords: book
zbMATH Keywords: Ramsey number
MaRDI profile type: Publication
OpenAlex ID: W1994864317
DOI: 10.1006/JCTB.1996.0055
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description: scientific article; zbMATH DE number 934823