Title

Saturation Numbers for Families of Ramsey-Minimal Graphs

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.

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