Ordered Ramsey numbers

详细信息    查看全文

• 作者：David Conlon^a ; ¹ ; ^{david.conlon@maths.ox.ac.uk} ; Jacob Fox^b ; ² ; ^{jacobfox@stanford.edu} ; Choongbum Lee^c ; ³ ; ^{cb_lee@math.mit.edu} ; Benny Sudakov^d ; ⁴ ; ^{benjamin.sudakov@math.ethz.ch}
• 关键词：Ramsey theory ; Ordered graphs ; Sparse graphs
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：122
• 期：Complete
• 页码：353-383
• 全文大小：588 K
• 卷排序：122

文摘

Given a labeled graph H   with vertex set {1,2,…,n}{1,2,…,n}, the ordered Ramsey number r<(H)r<(H) is the minimum N   such that every two-coloring of the edges of the complete graph on {1,2,…,N}{1,2,…,N} contains a copy of H with vertices appearing in the same order as in H. The ordered Ramsey number of a labeled graph H   is at least the Ramsey number r(H)r(H) and the two coincide for complete graphs. However, we prove that even for matchings there are labelings where the ordered Ramsey number is superpolynomial in the number of vertices. Among other results, we also prove a general upper bound on ordered Ramsey numbers which implies that there exists a constant c   such that r<(H)≤r(H)clog2⁡nr<(H)≤r(H)clog2⁡n for any labeled graph H   on vertex set {1,2,…,n}{1,2,…,n}.