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 Kn⊔Sk be a graph obtained by adding a new vertex v and joining v to k vertices of Kn. The star-critical Ramsey number r∗(G,H) is the smallest positive integer k such that any red/blue coloring of the edges of graph Kr−1⊔Sk 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 r∗(Fn,K4)=4n+2 where n≥4.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
