Translator Disclaimer
2019 On some edge Folkman numbers, small and large
Jenny M. Kaufmann, Henry J. Wickus, Stanisław P. Radziszowski
Involve 12(5): 813-822 (2019). DOI: 10.2140/involve.2019.12.813

Abstract

Edge Folkman numbers Fe(G1,G2;k) can be viewed as a generalization of more commonly studied Ramsey numbers. Fe(G1,G2;k) is defined as the smallest order of any Kk-free graph F such that any red-blue coloring of the edges of F contains either a red G1 or a blue G2. In this note, first we discuss edge Folkman numbers involving graphs Js=Kse, including the results Fe(J3,Kn;n+1)=2n1, Fe(J3,Jn;n)=2n1, and Fe(J3,Jn;n+1)=2n3. Our modification of computational methods used previously in the study of classical Folkman numbers is applied to obtain upper bounds on Fe(J4,J4;k) for all k>4.

Citation

Download Citation

Jenny M. Kaufmann. Henry J. Wickus. Stanisław P. Radziszowski. "On some edge Folkman numbers, small and large." Involve 12 (5) 813 - 822, 2019. https://doi.org/10.2140/involve.2019.12.813

Information

Received: 3 June 2018; Revised: 23 October 2018; Accepted: 29 November 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07072555
MathSciNet: MR3954297
Digital Object Identifier: 10.2140/involve.2019.12.813

Subjects:
Primary: 05C55

Keywords: Folkman numbers , Ramsey numbers

Rights: Copyright © 2019 Mathematical Sciences Publishers

JOURNAL ARTICLE
10 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.12 • No. 5 • 2019
MSP
Back to Top