Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs

DOI10.1016/j.jctb.2011.12.003zbMath1239.05096OpenAlexW1996822859MaRDI QIDQ412167

Bodo Lass

Publication date: 4 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jctb.2011.12.003

zbMATH Keywords

rootsHermite polynomialmatching polynomialindependence polynomialalgebra of set functionsclawfree graphsmehler formulamonomer dimer systemspartitions of sets

Mathematics Subject Classification ID

Graph polynomials (05C31) Exact enumeration problems, generating functions (05A15) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (5)

Laplacian matching polynomial of graphs ⋮ Independence polynomials and Alexander-Conway polynomials of plumbing links ⋮ Christoffel–Darboux Type Identities for the Independence Polynomial ⋮ Upper bounds for the independence polynomial of graphs at \(-1\) ⋮ Generalizations of the matching polynomial to the multivariate independence polynomial

Cites Work

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• Matching polynomials and duality
• On the location of roots of independence polynomials
• Characteristic polynomials of nonnegative integral square matrices and clique polynomials
• On the dependence polynomial of a graph
• The roots of the independence polynomial of a clawfree graph
• Zero-free regions for multivariate tutte polynomials (alias Potts-model partition functions) of graphs and matroids
• Hermite polynomials and a duality relation for matchings polynomials
• A combinational proof of the Mehler formula
• Clique polynomials and independent set polynomials of graphs
• Problems in algebraic combinatorics
• Homogeneous multivariate polynomials with the half-plane property
• Roots of independence polynomials of well covered graphs
• Graph colorings and related symmetric functions: ideas and applications: A description of results, interesting applications, and notable open problems.
• Average independence polynomials
• On the numbers of independent \(k\)-sets in a claw free graph
• Variations sur le thème \({E+\overline {E} = XY}\) (Variations on the theme \({E+\overline {E} = XY})\)
• The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma
• Theory of monomer-dimer systems
• The \(N\)-dimensional matching polynomial
• Dependence polynomials
• On Dependency Graphs and the Lattice Gas
• Acyclic orientations and the chromatic polynomial

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