Saturation Numbers for Families of Ramsey-Minimal Graphs

Authors

Guantao Chen, Georgia State UniversityFollow
Micheal Ferrara, University of Colorado at DenverFollow
Ronald Gould, Emory UniversityFollow
Colton Magnant, Georgia Southern UniversityFollow
John Schmitt, Middlebury CollegeFollow

Document Type

Article

Publication Date

2011

Publication Title

Journal of Combinatorics

DOI

10.4310/JOC.2011.v2.n3.a5

ISSN

2150-959X

Abstract

Given a family of graphs F, a graph G is F-saturated if no element of F is a subgraph of G, but for any edge e in G,someelement of F is a subgraph of G + e.Letsat(n, F) denote the minimum number of edges in an F-saturated graph of order n.

For graphs G, H1,...,Hk, we write that G → (H1,...,Hk)if every k-coloring of E(G) contains a monochromatic copy of Hi in color i for some i. A graph G is (H1,...,Hk)-Ramsey-minimal if G → (H1,...,Hk) but for any e ∈ G,(G − e) →/→ (H1,...,Hk). Let Rmin(H1,...,Hk) denote the family of (H1,...,Hk)-Ramsey-minimal graphs.

Recommended Citation

Chen, Guantao, Micheal Ferrara, Ronald Gould, Colton Magnant, John Schmitt. 2011. "Saturation Numbers for Families of Ramsey-Minimal Graphs." Journal of Combinatorics, 2 (3): 435-455. doi: 10.4310/JOC.2011.v2.n3.a5
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/281