New upper bounds for Ramsey numbers of books

A book Bn is a graph which consists of n triangles sharing a common edge. Rousseau and Sheehan (1978) conjectured that r(Bm,Bn)≤2(m+n+1)+c some constant c>0. Let m=⌊αn⌋ where 0

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Bibliographic Details
Published in:European journal of combinatorics 2024-01, Vol.115, p.103785, Article 103785
Main Authors: Chen, Xun, Lin, Qizhong
Format: Article
Language:English
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Summary:A book Bn is a graph which consists of n triangles sharing a common edge. Rousseau and Sheehan (1978) conjectured that r(Bm,Bn)≤2(m+n+1)+c some constant c>0. Let m=⌊αn⌋ where 0
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2023.103785