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Finite dualities and map-critical graphs on a fixed surface

2012
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Journal of combinatorial theory. Series B (Print)
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Let K be a class of graphs. Then, K is said to have a finite duality if there exists a pair (F, U ), where U ∈ K and F is a finite set of graphs, such that for any graph G in K we have G ≤ U if and only if F ≤ G for all F ∈ F (" ≤ " is the homomorphism order). We prove that the class of planar graphs has no finite duality except for two trivial cases. We also prove that a 5-colorable toroidal graph U obtains a finite duality on a given fixed surface if and only if the core of U is K 5 . In a

doi:10.1016/j.jctb.2011.06.001
fatcat:qxftndmv5jclthwoccyeaaoyv4