On Path Convex Ramsey Numbers

Jayawardene, Chula J.; Rousseau, Cecil C.; Harborth, Heiko

doi:10.1002/jgt.22126

Journal of Graph Theory

2017

DOI: 10.1002/jgt.22126

|View full text |Cite

On Path Convex Ramsey Numbers

Chula J. Jayawardene

Cecil C. Rousseau

Heiko Harborth

Abstract: In this article, we will first find the path convex Ramsey numbers for two-colorings. Then using this, we will deduce some bounds for path convex Ramsey numbers for multicolorings. Next, we will find the convex Ramsey numbers for convex paths versus any graph containing a convex cycle, for convex paths versus stars, and for convex cycles versus stars.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Book1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 15 publications

(15 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices

Jayawardene

2020

Handbook of Research on Advanced Applications of Graph Theory in Modern Society

View full text Add to dashboard Cite

A popular area of graph theory is based on a paper written in 1930 by F. P. Ramsey titled “On a Problem on Formal Logic.” A theorem which was proved in his paper triggered the study of modern Ramsey theory. However, his premature death at the young age of 26 hindered the development of this area of study at the initial stages. The balanced size multipartite Ramsey number mj (H,G) is defined as the smallest positive number s such that Kj×s→ (H,G). There are 36 pairs of (H, G), when H, G represent connected graphs on four vertices (as there are only 6 non-isomorphic connected graphs on four vertices). In this chapter, the authors find mj (H, G) exhaustively for all such pairs in the tripartite case j=3, and in the quadpartite case j=4, excluding the case m4 (K4,K4). In this case, the only known result is that m4 (K4,K4) is greater than or equal to 4, since no upper bound has been found as yet.

show abstract

Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices

Jayawardene

2020

Handbook of Research on Advanced Applications of Graph Theory in Modern Society

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On Path Convex Ramsey Numbers

Cited by 1 publication

References 15 publications

Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices

Tripartite and Quadpartite Size Ramsey Numbers for All Pairs of Connected Graphs on Four Vertices

Contact Info

Product

Resources

About