2011/01/01 by Zhi-Hong Sun, Sun, Zhi-Hong
Computer Science · Mathematics · #05C35 #05C55 #05D10 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #math.CO #msc:05C35 #msc:05C55 #msc:05D10
paper · pdf · doi:10.48550/arxiv.1101.0334
16 pages
openalex publication_date 2011/01/01 · arxiv created 2014/11/05 · arxiv updated 2014/11/06 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let n,r,k,s be positive integers with n,k≥ 2. The generalized Ramsey number R(n,r;k,s) is the smallest positive integer p such that for every graph G of order p, either G contains a subgraph induced by n vertices with at most r-1 edges, or the complement G of G contains a subgraph induced by k vertices with at most s-1 edges. In this paper we completely determine R(n,n(n-1)/2-r;k,1) for n≥ 4 and r≤ n-2, and pose several conjectures on Ramsey numbers.