Homomorphisms of Products of Graphs into Graphs Without Four Cycles
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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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