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The Dichromate and Orientations of a Graph
Published online by Cambridge University Press: 20 November 2018
Extract
Internal and external activities are defined for any orientation of a graph relative to a fixed labelling of its edges. It is shown that the number of such orientations of
having internal activity r and external activity s is 2r+sXrs where Xrs is the coefficient of xrys in the dichromate
It follows that the number of orientations of
in which the resulting digraph
is acyclic is given by
, where
is the chromatic polynomial associated with
.
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- Copyright © Canadian Mathematical Society 1977
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