Edge colouring models for the Tutte polynomial and related graph invariants

Details Edge colouring models for the Tutte polynomial and related graph invariants Edge colouring models for the Tutte polynomial and related graph invariants

2007-07-16

arxiv.org/abs/0707.2297v1

Mathematics

Combinatorics

33 pages

Scientific paper

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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