Chromatic functors of graphs
Chromatic functors of graphs
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图的色函子
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Yoshinaga
中科院分区：
文献类型：
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作者：
M. Yoshinaga
具有公共色多项式的有限图具有相同数量的正则n -着色。一个自然的问题是，在正则的n -颜色之间是否存在自然的双射。我们用函数公式来解决这个问题。设$G$为简单图。然后对于每一个集合X，我们可以关联一组X的颜色。这定义了一个函子，“色函子”，它来自于对自身有注入的集合的范畴。第一个主要结果证明两个有限图确定同构的色函子当且仅当它们具有相同的色多项式。
Finite graphs that have a common chromatic polynomial have the same number of regular $n$-colorings. A natural question is whether there exists a natural bijection between regular $n$-colorings. We address this question using a functorial formulation. Let $G$ be a simple graph. Then for each set $X$ we can associate a set of $X$-colorings. This defines a functor, "chromatic functor" from the category of sets with injections to itself. The first main result verifies that two finite graphs determine isomorphic chromatic functors if and only if they have the same chromatic polynomial.
Chromatic functors can be defined for arbitrary, possibly infinite, graphs. This fact enables us to investigate functorial chromatic theory for infinite graphs. We prove that chromatic functors satisfy the Cantor-Bernstein-Schr\"oder property. We also prove that countable connected trees determine isomorphic chromatic functors. Finally, we present a pair of infinite graphs that determine non-isomorphic chromatic functors.
影响因子：
1.3
作者：
D. Kozlov
通讯作者：
D. Kozlov