Type: Article

Ramsey theory for highly connected monochromatic subgraphs

Bergfalk, J, Hrusak, M; Shelah, S.;

Abstract:

An infinite graph is highly connected if the complement of anysubgraph of smaller size is connected. We consider weaker versions of Ramsey’sTheorem asserting that in any coloring of the edges of a complete graph thereexist large highly connected subgraphs all of whose edges are colored by the samecolor