Ramsey families which exclude a graph


For graphsA andB the relationA→(B) 1r means that for everyr-coloring of the vertices ofA there is a monochromatic copy ofB inA. Forb (G) is the family of graphs which do not embedG. A familyℱof graphs is Ramsey if for all graphsB∈ℱthere is a graphA∈ℱsuch thatA→(B) 1r . The only graphsG for which it is not known whether Forb (G) is Ramsey are graphs which have a cutpoint adjacent to every other vertex except one. In this paper we prove for a large subclass of those graphsG, that Forb (G) does not have the Ramsey property.

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This research has been supported in part by NSERC grant 69-1325.

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Rödl, V., Sauer, N. & Zhu, X. Ramsey families which exclude a graph. Combinatorica 15, 589–596 (1995). https://doi.org/10.1007/BF01192529

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Mathematics Subject Classification (1991)

  • 05 C 55