| Meno: | Matúą
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| Priezvisko: | Matok
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| Názov: | Minimisation of the signed four colour theorem's counterexample
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| Vedúci: | RNDr. Ing. Frantiąek Kardoą, PhD.
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| Rok: | 2023
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| Kµúčové slová: | counterexample, cubic graph, signed planar graph, dual graph
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| Abstrakt: | A signed graph is a generalisation of the traditional concept of a graph. A conjecture that the four colour theorem for planar graphs holds for signed planar graphs as well was brought up Mačajova, Raspaud and ©koviera. It got soon disputed by Kardoą and Narboni who constructed a counterexample. Our goal is to find a smaller counterexample by studying the properties of the dual. We implement an exhaustive computer-assisted search that verifies the properties on induced subgraphs of the dual.
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