论文标题
三立方图的3边色的反射着色络合物
Reflexive coloring complexes for 3-edge-colorings of cubic graphs
论文作者
论文摘要
给定3色图$ x $，3色的复合体$ b（x）$是其顶点的图形，其所有独立集作为颜色类别出现，大约3色$ x $。如果$ c $和$ d $一起出现在V（b（x））$中的两个颜色类$ c，d \ in V（b（x））$连接在一起，则以$ x $的3颜色出现。图$ b（x）$是3色。 $ b（b（x））$同构至$ x $的图被称为反射图。在本文中，我们考虑了三种图形的3边色，我们允许半边缘。然后，我们考虑其线图的三色复合物。本文的主要结果是令人惊讶的结果是，任何连接的立方三角形外平面图的线图都是反射性的。我们还展示了其他一些有趣的反射线图。
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 $C,D \in V(B(X))$ 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 the 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.
