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Reflexive coloring complexes for 3-edge-colorings of cubic graphs
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-01-25 , DOI: 10.1016/j.disc.2021.112309
Fiachra Knox , Bojan Mohar , Nathan Singer

Given a 3-colorable graph X, the 3-coloring complex B(X) is the graph whose vertices are all the independent sets which occur as color classes in some 3-coloring of X. Two color classes C,DV(B(X)) are joined by an edge if C and D appear together in a 3-coloring of X. The graph B(X) is 3-colorable. Graphs for which B(B(X)) is isomorphic to X are termed reflexive graphs. In this paper, we consider 3-edge-colorings of cubic graphs for which we allow half-edges. Then we consider the 3-coloring complexes of their line graphs. The main result of this paper is a surprising outcome that the line graph of any connected cubic triangle-free outerplanar graph is reflexive. We also exhibit some other interesting classes of reflexive line graphs.



中文翻译:

立方图的3边着色的自反着色复合体

给定一个三色图 X,三色复合物 X 是图形,其顶点是所有独立的集合,在颜色的某些3色中作为颜色类出现 X。两种颜色等级CdVX 如果被边缘连接 Cd 一起以3种颜色出现 X。图X是3色的。的图形X 同构 X被称为自反图。在本文中,我们考虑三次图的3边着色,允许我们使用半边。然后我们考虑其线图的3色复合体。本文的主要结果是令人惊讶的结果,即任何连接的立方无三角形外平面图的线图都是自反的。我们还展示了自反折线图的其他一些有趣的类别。

更新日期:2021-01-25
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