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arXiv · 0707.2297

Edge colouring models for the Tutte polynomial and related graph invariants

Andrew J. Goodall
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Abstract

For integer q>1, we derive edge q-colouring models for (i) the Tutte polynomial of a graph G on the hyperbola H_q, (ii) the symmetric weight enumerator of the set of group-valued q-flows of G, and (iii) a more general vertex colouring model partition function that includes these polynomials and the principal specialization order q of Stanley's symmetric monochrome polynomial. In the second half of the paper we exhibit a family of non-symmetric edge q-colouring models defined on k-regular graphs, whose partition functions for q >= k each evaluate the number of proper edge k-colourings of G when G is Pfaffian.

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Andrew J. Goodall. 2007-07-16. Edge colouring models for the Tutte polynomial and related graph invariants. https://arxiv.org/abs/0707.2297

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