Abstract

A graph G is totally connected if both G and Ḡ (its complement) are connected. The connected Ramsey number rc(F, H) is the smallest integer k ⩾ 4 so that if G is a totally connected graph of order k then either F ⊂ G or H ⊂ Ḡ. We show that if neither of F nor H contains a bridge, then rc = r(F, H), the usual generalized Ramsey number of F and H. We compute rc (PmPm), the connected Ramsey number for paths.

Full Text
Paper version not known

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 call

Disclaimer: 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.