Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777346 | European Journal of Combinatorics | 2018 | 7 Pages |
Abstract
For given simple graphs G1,G2,â¦,Gt, the Ramsey number R(G1,G2,â¦,Gt) is the smallest positive integer n such that if the edges of the complete graph Kn are partitioned into t disjoint color classes giving t graphs H1,H2,â¦,Ht, then at least one Hi has a subgraph isomorphic to Gi. In this paper, for positive integers t1,t2,â¦,ts and n1,n2,â¦,nc the Ramsey number R(St1,St2,â¦,Sts,n1K2,n2K2,â¦,ncK2) is computed exactly, where nK2 denotes a matching (stripe) of size n, i.e., n pairwise disjoint edges and Sn is a star with n edges. This result generalizes and strengthens significantly a well-known result of Cockayne and Lorimer and also a known result of Gyárfás and Sárközy.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
G.R. Omidi, G. Raeisi, Z. Rahimi,