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arXiv · 1501.06105

Iterated claws have real-rooted genus polynomials

J. L. Gross·T. Mansour·T. W. Tucker·D. G. L. Wang
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Abstract

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 operations are adding a claw and adding a 3-cycle, 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.

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BibTeXRIS

J. L. Gross, T. Mansour, T. W. Tucker, D. G. L. Wang. 2015-01-25. Iterated claws have real-rooted genus polynomials. https://arxiv.org/abs/1501.06105

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