Discrete Mathematics
On the numbers of independent k-sets in a claw free graph
Journal of Combinatorial Theory Series B
Clique polynomials and independent set polynomials of graphs
Selected papers of the 13th British Combinatorial Conference on British combinatorial conference
Discrete Mathematics - selected papers in honor of Adriano Garsia
Roots of Independence Polynomials of Well Covered Graphs
Journal of Algebraic Combinatorics: An International Journal
On the Location of Roots of Independence Polynomials
Journal of Algebraic Combinatorics: An International Journal
Average independence polynomials
Journal of Combinatorial Theory Series B
On the Charney-Davis and Neggers-Stanley conjectures
Journal of Combinatorial Theory Series A
Matroid representation of clique complexes
Discrete Applied Mathematics
On the roots of independence polynomials of almost all very well-covered graphs
Discrete Applied Mathematics
The independence polynomial of rooted products of graphs
Discrete Applied Mathematics
Independence polynomials of k-tree related graphs
Discrete Applied Mathematics
On the unimodality of independence polynomials of some graphs
European Journal of Combinatorics
Independent Sets of Maximum Weight in Apple-Free Graphs
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Optimization
Independence polynomials of some compound graphs
Discrete Applied Mathematics
Mehler formulae for matching polynomials of graphs and independence polynomials of clawfree graphs
Journal of Combinatorial Theory Series B
On the edge cover polynomial of a graph
European Journal of Combinatorics
Discrete Applied Mathematics
Lee-Yang theorems and the complexity of computing averages
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The independence polynomial of a graph G is the polynomial @?"Ax^|^A^|, summed over all independent subsets A@?V(G). We prove that if G is clawfree, then all the roots of its independence polynomial are real. This extends a theorem of Heilmann and Lieb [O.J. Heilmann, E.H. Lieb, Theory of monomer-dimer systems, Comm. Math. Phys. 25 (1972) 190-232], answering a question posed by Hamidoune [Y.O. Hamidoune, On the numbers of independent k-sets in a clawfree graph, J. Combin. Theory Ser. B 50 (1990) 241-244] and Stanley [R.P. Stanley, Graph colorings and related symmetric functions: Ideas and applications, Discrete Math. 193 (1998) 267-286].