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- W1996822859 abstract "The independence polynomial of a graph G is the polynomial ∑Ix|I|, summed over all independent subsets I⊆V(G). We show that if G is clawfree, then there exists a Mehler formula for its independence polynomial. This was proved for matching polynomials in Lass (2004) [19] and extends the combinatorial proof of the Mehler formula found by Foata (1978) [9]. It implies immediately that all the roots of the independence polynomial of a clawfree graph are real, answering a question posed by Hamidoune (1990) [14] and Stanley (1998) [28] and solved by Chudnovsky and Seymour (2007) [6]. We also prove a Mehler formula for the multivariate matching polynomial, extending results of Lass (2004) [19]." @default.
- W1996822859 created "2016-06-24" @default.
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- W1996822859 date "2012-03-01" @default.
- W1996822859 modified "2023-09-30" @default.
- W1996822859 title "Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs" @default.
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- W1996822859 doi "https://doi.org/10.1016/j.jctb.2011.12.003" @default.
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