A Ramsey property of random regular and k-out graphs

Authors

• Michael Anastos, Carnegie Mellon University
• Deepak Bal, Montclair State UniversityFollow

Document Type

Preprint

Publication Date

3-1-2020

Journal / Book Title

Journal of Graph Theory

Abstract

In this study we consider a Ramsey property of random d-regular graphs, g(n, d). Let r ≥ 2 be fixed. Then w.h.p. the edges of g(n, 2r) can be colored such that every monochromatic component has order o (n). On the other hand, there exists a constant γ > 0 such that w.h.p., every r-coloring of the edges of g(n, 2r + 1) must contain a monochromatic cycle of length at least γn. We prove an analogous result for random k -out graphs.

DOI

10.1002/jgt.22491

MSU Digital Commons Citation

Anastos, Michael and Bal, Deepak, "A Ramsey property of random regular and k-out graphs" (2020). Department of Mathematics Faculty Scholarship and Creative Works. 214.
https://digitalcommons.montclair.edu/mathsci-facpubs/214

Rights

This is an uncorrected preprint of: Anastos, M., & Bal, D. (2020). A Ramsey property of random regular and k‐out graphs. Journal of Graph Theory, 93(3), 363-371.