Polynomials associated with nowhere-zero flows

DOI10.1006/jctb.2001.2081zbMath1027.05080OpenAlexW2167712310MaRDI QIDQ1850590

Martin Kochol

Publication date: 10 December 2002

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

Full work available at URL: https://doi.org/10.1006/jctb.2001.2081

zbMATH Keywords

flows in graphs

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Enumeration in graph theory (05C30) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (24)

A Tutte Polynomial for Maps ⋮ The number of nowhere-zero flows on graphs and signed graphs ⋮ Many faces of symmetric edge polytopes ⋮ Orientations, lattice polytopes, and group arrangements. II: Modular and integral flow polynomials of graphs ⋮ Dualities and reciprocities on graphs on surfaces ⋮ A note on counting flows in signed graphs ⋮ The parity Hamiltonian cycle problem ⋮ Bounds on the coefficients of tension and flow polynomials ⋮ Dual complementary polynomials of graphs and combinatorial-geometric interpretation on the values of Tutte polynomial at positive integers ⋮ Tension-flow polynomials on graphs ⋮ Nowhere-harmonic colorings of graphs ⋮ Ehrhart theory, modular flow reciprocity, and the Tutte polynomial ⋮ Orientations, lattice polytopes, and group arrangements. III: Cartesian product arrangements and applications to Tutte type polynomials ⋮ Nowhere-zero \(\vec{k}\)-flows on graphs ⋮ Inside-out polytopes ⋮ Polynomial algorithms for canonical forms of orientations ⋮ Binomial inequalities for chromatic, flow, and tension polynomials ⋮ A bijection for Eulerian-equivalence classes of totally cyclic orientations ⋮ Bounds of characteristic polynomials of regular matroids ⋮ A note on flow polynomials of graphs ⋮ The Parity Hamiltonian Cycle Problem in Directed Graphs ⋮ Flow polynomials of a signed graph ⋮ Enumerating colorings, tensions and flows in cell complexes ⋮ Tension polynomials of graphs

Cites Work

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• Superposition and constructions of graphs without nowhere-zero \(k\)-flows
• Integer flows
• Hypothetical complexity of the nowhere-zero 5-flow problem
• Lectures on Polytopes
• Lectures on matroids
• Sur un probl?me de g?om?trie diophantienne lin?aire. I. Poly?dres et r?seaux.
• A theorem on three-coloring the edges of a trivalent graph
• On the Imbedding of Linear Graphs in Surfaces
• A Contribution to the Theory of Chromatic Polynomials

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