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Discussiones Mathematicae Graph Theory 32(4) (2012)
617-627
DOI: https://doi.org/10.7151/dmgt.1630
4-chromatic Koester Graphs
| Andrey A. Dobrynin and Leonid S. Mel'nikov
Sobolev Institute of Mathematics |
Abstract
Let G be a simple 4-regular plane graph and let S be a decomposition of G into edge-disjoint cycles. Suppose that every two adjacent edges on a face belong to different cycles of S. Such a graph G arises as a superposition of simple closed curves in the plane with tangencies disallowed. Studies of coloring of graphs of this kind were originated by Grötzsch. Two 4-chromatic graphs generated by circles in the plane were constructed by Koester in 1984 [10,11,12]. Until now, no other examples of such graphs were known. We present fourteen new 4-chromatic graphs generated by circles in the plane.
Keywords: planar graph, 4-critical graph, Grötzsch-Sachs graph, Koester graph
2010 Mathematics Subject Classification: 05C10, 05C15.
References
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Received 26 July 2011
Revised 15 November 2011
Accepted 18 November 2011
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