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- W4300874210 abstract "Given a group $G$ of automorphisms of a graph $Gamma$, the orbital chromatic polynomial $OP_{Gamma,G}(x)$ is the polynomial whose value at a positive integer $k$ is the number of orbits of $G$ on proper $k$-colorings of $Gamma.$ In cite{Cameron}, Cameron et. al. explore the roots of orbital chromatic polynomials, and in particular prove that orbital chromatic roots are dense in $mathbb{R}$, extending Thomassen's famous result (see cite{Thomassen}) that chromatic roots are dense in $[frac{32}{27},infty)$. Cameron et al cite{Cameron} further conjectured that the real roots of the orbital chromatic polynomial of any graph are bounded above by the largest real root of its chromatic polynomial. We resolve this conjecture in the negative, and provide a process for generating families of counterexamples. We additionally show that the answer is true for various classes of graphs, including many outerplanar graphs." @default.
- W4300874210 created "2022-10-04" @default.
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- W4300874210 date "2013-10-14" @default.
- W4300874210 modified "2023-10-16" @default.
- W4300874210 title "Chromatic Bounds On Orbital Chromatic Roots" @default.
- W4300874210 doi "https://doi.org/10.48550/arxiv.1310.3792" @default.
- W4300874210 hasPublicationYear "2013" @default.
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