Geodesic
Iterated claws have real-rooted genus polynomials
Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 255-268.

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We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertex-amalgamation or iterative edge-amalgamation of graphs that satisfy a commonly observable condition on their partitioned genus distributions, even though it had been proved previously that iterative amalgamation does not always preserve real-rootedness of the genus polynomial of the iterated graph. In this paper, the iterated topological operation is adding a claw, rather than vertex- or edge-amalgamation. Our analysis here illustrates some advantages of employing a matrix representation of the transposition of a set of productions.
DOI : 10.26493/1855-3974.538.86e
Keywords: Topological graph theory, graph genus polynomials, log-concavity, real-rootedness 
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Jonathan L. Gross; Toufik Mansour; Thomas W. Tucker; David G. L. Wang. Iterated claws have real-rooted genus polynomials. Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 255-268. doi : 10.26493/1855-3974.538.86e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.538.86e/

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