Homomorphism bounded classes of graphs

Authors:
Timothy Marshall;Reza Nasraser;Jaroslav Nešetřil
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Praha, Czech Republic;Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada;Department of Applied Mathematics and Institute for Theoretical Computer Science (ITI), Charles University, Praha, Czech Republic
Venue:
European Journal of Combinatorics
Year:
2006

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Abstract

A class C of graphs is said to be H-bounded if each graph in the class C admits a homomorphism to H. We give a general necessary and sufficient condition for the existence of bounds with special local properties. This gives a new proof of the Häggkvist-Hell theorem [R. Häggkvist, P. Hell, Universality of A-mote graphs, European J. Combin. 14 (1993) 23-27] and implies several cases of the existence of triangle free bounds for planar graphs.