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Saturation Numbers for Families of Ramsey-Minimal Graphs
Journal of Combinatorics
  • Guantao Chen, Georgia State University
  • Micheal Ferrara, University of Colorado at Denver
  • Ronald Gould, Emory University
  • Colton Magnant, Georgia Southern University
  • John Schmitt, Middlebury College
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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.

Citation Information
Guantao Chen, Micheal Ferrara, Ronald Gould, Colton Magnant, et al.. "Saturation Numbers for Families of Ramsey-Minimal Graphs" Journal of Combinatorics Vol. 2 Iss. 3 (2011) p. 435 - 455 ISSN: 2150-959X
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