Fraternal augmentations, arrangeability and linear Ramsey numbers

Authors:
Jaroslav Nešetřil;Patrice Ossona de Mendez
Affiliations:
Department of Applied Mathematics, Charles University, Malostranské nám.25, 11800 Praha 1, Czech Republic and Institute of Theoretical Computer Science (ITI), Malostranské nám. ...;Centre d'Analyse et de Mathématiques Sociales, CNRS, UMR 8557, 54 Bd Raspail, 75006 Paris, France
Venue:
European Journal of Combinatorics
Year:
2009

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Abstract

We relate the notions of arrangeability and admissibility to bounded expansion classes and prove that these notions can be characterized by @?"1(G). (The Burr-Erdos conjecture relates to @?"0(G).) This implies the linearity of the Ramsey number and the bounded game chromatic number for some new classes of graphs.