%0 Journal Article %1 chudnovsky07 %A Chudnovsky, Maria %A Seymour, Paul %D 2007 %J Journal of Combinatorial Theory, Series B %K graph.theory independence interlacing polynomial real-rooted root root-free %N 3 %P 350 -- 357 %R 10.1016/j.jctb.2006.06.001 %T The Roots of the Independence Polynomial of a Clawfree Graph %V 97 %X The independence polynomial of a graph G is the polynomial ∑ A x | 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.

@article{chudnovsky07, abstract = {The independence polynomial of a graph G is the polynomial ∑ A x | 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]. }, added-at = {2015-06-08T09:19:36.000+0200}, author = {Chudnovsky, Maria and Seymour, Paul}, biburl = {https://www.bibsonomy.org/bibtex/2dff0aba8ed3a60c0dcf30ef65cd58e8f/ytyoun}, doi = {10.1016/j.jctb.2006.06.001}, interhash = {f9e66b76331eee4d7cb5180387690053}, intrahash = {dff0aba8ed3a60c0dcf30ef65cd58e8f}, issn = {0095-8956}, journal = {Journal of Combinatorial Theory, Series B }, keywords = {graph.theory independence interlacing polynomial real-rooted root root-free}, number = 3, pages = {350 -- 357}, timestamp = {2017-03-17T10:29:09.000+0100}, title = {The Roots of the Independence Polynomial of a Clawfree Graph }, volume = 97, year = 2007 }