Biased graphs. III: Chromatic and dichromatic invariants

DOI10.1006/jctb.1995.1025zbMath0857.05088OpenAlexW2080817296MaRDI QIDQ1892851

Thomas Zaslavsky

Publication date: 4 July 1995

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/e707496a08effec6c86be527b51ccbeb23b1f011

zbMATH Keywords

root systemssupersolvabilitydichromatic polynomialWhitney numbersbiased graphDowling latticesbias matroidbalanced circlesseries-parallel networkdeletion-contraction invariancelift matroidsWhitney number polynomials

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35) Coloring of graphs and hypergraphs (05C15) Graph theory (05C99)

Related Items (20)

Enumeration of extensions of the cycle matroid of a complete graph ⋮ Generalized signed graphs of large girth and large chromatic number ⋮ A bibliography on chromatic polynomials ⋮ A Generalisation of the Matroid Lift Construction ⋮ On the determinant of the Laplacian matrix of a complex unit gain graph ⋮ Biased expansions of biased graphs and their chromatic polynomials ⋮ On colorings and orientations of signed graphs ⋮ \(4\)-colouring of generalized signed planar graphs ⋮ Tutte's dichromate for signed graphs ⋮ A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from \(\{\pm 1,{\pm}i\}\) ⋮ Biased graphs. II: The three matroids ⋮ Concepts of signed graph coloring ⋮ Colouring of \(S\)-labelled planar graphs ⋮ Lindström's conjecture on a class of algebraically non-representable matroids ⋮ Minimal blocks of binary even-weight vectors ⋮ Totally frustrated states in the chromatic theory of gain graphs ⋮ Describing quasi-graphic matroids ⋮ Biased graphs. I: Bias, balance, and gains ⋮ Quasigroup associativity and biased expansion graphs ⋮ Lattice points in orthotopes and a huge polynomial Tutte invariant of weighted gain graphs

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