Graph colorings, flows and arithmetic Tutte polynomial

Details Graph colorings, flows and arithmetic Tutte polynomial Graph colorings, flows and arithmetic Tutte polynomial

2011-08-29

arxiv.org/abs/1108.5537v1

Mathematics

Combinatorics

19 pages, 12 figures

Scientific paper

We introduce the notions of arithmetic colorings and arithmetic flows over a graph with labelled edges, which generalize the notions of colorings and flows over a graph. We show that the corresponding arithmetic chromatic polynomial and arithmetic flow polynomial are given by suitable specializations of the associated arithmetic Tutte polynomial, generalizing classical results of Tutte.

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