Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Contraction-deletion invariants for graphs
Journal of Combinatorial Theory Series B
Bounds on the Complex Zeros of (Di)Chromatic Polynomials and Potts-Model Partition Functions
Combinatorics, Probability and Computing
A Tutte Polynomial for Coloured Graphs
Combinatorics, Probability and Computing
Counting connected graphs inside-out
Journal of Combinatorial Theory Series B
Truncating the Loop Series Expansion for Belief Propagation
The Journal of Machine Learning Research
The k-core and branching processes
Combinatorics, Probability and Computing
The bivariate Ising polynomial of a graph
Discrete Applied Mathematics
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We introduce two graph polynomials and discuss their properties. One is a polynomial of two variables whose investigation is motivated by the performance analysis of the Bethe approximation of the Ising partition function. The other is a polynomial of one variable that is obtained by the specialization of the first one. It is shown that these polynomials satisfy deletion–contraction relations and are new examples of the V-function, which was introduced by Tutte (Proc. Cambridge Philos. Soc.43, 1947, p. 26). For these polynomials, we discuss the interpretations of special values and then obtain the bound on the number of sub-coregraphs, i.e., spanning subgraphs with no vertices of degree one. It is proved that the polynomial of one variable is equal to the monomer–dimer partition function with weights parametrized by that variable. The properties of the coefficients and the possible region of zeros are also discussed for this polynomial.