Homomorphisms of Products of Graphs into Graphs Without Four Cycles

Given two graphs A and G, we write if there is a homomorphism of A to G and if there is no such homomorphism. The graph G is -free if, whenever both a and c are adjacent to b and d, then a = c or b = d. We will prove that if A and B are connected graphs, each containing a triangle and if G is a -free graph with and , then (here "" denotes the categorical product).

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Received August 31, 1998/Revised April 19, 2000

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ID="†" Supported by NSERC of Canada Grant #691325.

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Delhommé, C., Sauer, N. Homomorphisms of Products of Graphs into Graphs Without Four Cycles. Combinatorica 22, 35–46 (2002). https://doi.org/10.1007/s004930200002

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  • AMS Subject Classification (2000) Classes:  05C15