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- W1882159253 abstract "Finite graphs that have a common 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 functors if and only if they have the same polynomial. Chromatic functors can be defined for arbitrary, possibly infinite, graphs. This fact enables us to investigate functorial theory for infinite graphs. We prove that functors satisfy the Cantor-Bernstein-Schroder property. We also prove that countable connected trees determine isomorphic functors. Finally, we present a pair of infinite graphs that determine non-isomorphic functors." @default.
- W1882159253 created "2016-06-24" @default.
- W1882159253 creator A5039026089 @default.
- W1882159253 date "2015-07-23" @default.
- W1882159253 modified "2023-09-27" @default.
- W1882159253 title "Chromatic functors of graphs" @default.
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