Parametrized Tutte polynomials of graphs and matroids

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Abstract
  • We generalize and unify results on parametrized and coloured Tutte polynomials of graphs and matroids due to Zaslavsky, and Bollobas and Riordan. We give a generalized Zaslavsky-Bollobas-Riordan theorem that characterizes parametrized contraction-deletion functions on minor-closed classes of matroids, as well as the modifications necessary to apply the discussion to classes of graphs. In general, these parametrized Tutte polynomials do not satisfy analogues of all the familiar properties of the classical Tutte polynomial. We give conditions under which they do satisfy corank-nullity formulas, and also conditions under which they reflect the structure of series-parallel connections.
TitleParametrized Tutte polynomials of graphs and matroids
CreatorEllis-Monaghan, J. A.
Traldi, Lorenzo
PublisherCombinatorics, Probability and Computing
Academic DepartmentMathematics
DivisionNatural Sciences
OrganizationLafayette College
Date Issued2006
Date Available2010-04-21T20:28:17Z
TypeArticle
LanguageEnglish
Bibliographic CitationEllis-Monaghan, J. A. and L. Traldi. (2006) "Parametrized Tutte polynomials of graphs and matroids." Combinatorics, Probability and Computing 15: 835–854.
Standard IdentifierHandle 10385/651
DOI 10.1017/S0963548306007656
Permalinkhttp://hdl.handle.net/10385/651
Rights Statement In Copyright In Copyright
Rights HoldersCambridge University Press
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