4-chromatic edge critical Grötzsch-Sachs graphs |
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Authors: | A.A. Dobrynin,L.S. Mel&rsquo nikov |
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Affiliation: | Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia |
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Abstract: | Let G be a 4-regular plane graph and suppose that G has a cycle decomposition S (i.e., each edge of G is in exactly one cycle of the decomposition) with every pair of adjacent edges on a face always in different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Two 4-chromatic edge critical graphs of order 48 generated by four curves are presented. |
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Keywords: | Planar graphs Vertex coloring Chromatic number 4-critical graphs Grö tzsch-Sachs graphs |
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