Tutte polynomial expansions for 2-separable graphs

Authors:
Douglas R. Woodall
Affiliations:
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
Venue:
Discrete Mathematics
Year:
2002

Citing 3
Cited 3

Chromatic polynomials of homeomorphism classes of graphs

Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
The Tutte polynomial for homeomorphism classes of graphs

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Abstract

Let G be a graph obtained from a graph G with no loops or coloops by replacing each edge e = uw of G by a connected graph He that has only the vertices u and w in common with the rest of G. Two mutually dual formulas are proved for the Tutte polynomial of G in terms of parameters of the graphs He and (in the one case) flow polynomials of subgraphs of G or (in the other case) tension polynomials of contractions of G. This generalizes the results of Read and Whitehead on homeomorphism classes of graphs.