Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949793 | Discrete Applied Mathematics | 2017 | 7 Pages |
Abstract
For two graphs G and H, the Ramsey number r(G,H) is the smallest positive integer r, such that any red/blue coloring of the edges of graph Kr contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H. Let Sk=K1,k be a star of order k+1 and KnâSk be a graph obtained by adding a new vertex v and joining v to k vertices of Kn. The star-critical Ramsey number râ(G,H) is the smallest positive integer k such that any red/blue coloring of the edges of graph Krâ1âSk contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H where r=r(G,H). In this paper, it is shown that râ(Fn,K4)=4n+2 where nâ¥4.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Sh. Haghi, H.R. Maimani, A. Seify,