Chromatic Bounds on Orbital Chromatic Roots
نویسندگان
چکیده
منابع مشابه
Chromatic Bounds on Orbital Chromatic Roots
Given a group G of automorphisms of a graph Γ, the orbital chromatic polynomial OPΓ,G(x) is the polynomial whose value at a positive integer k is the number of orbits of G on proper k-colorings of Γ. Cameron and Kayibi introduced this polynomial as a means of understanding roots of chromatic polynomials. In this light, they posed a problem asking whether the real roots of the orbital chromatic ...
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The chromatic polynomial PΓ(x) of a graph Γ is a polynomial whose value at the positive integer k is the number of proper kcolourings of Γ. If G is a group of automorphisms of Γ, then there is a polynomial OPΓ,G(x), whose value at the positive integer k is the number of orbits of G on proper k-colourings of Γ. It is known there are no real negative chromatic roots, but they are dense in [ 27 ,∞...
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For any positive integer n, let Gn denote the set of simple graphs of order n. For any graph G in Gn, let P(G; ) denote its chromatic polynomial. In this paper, we -rst show that if G ∈Gn and (G)6 n− 3, then P(G; ) is zero-free in the interval (n − 4 + =6 − 2= ;+∞), where = (108 + 12√93)1=3 and =6 − 2= (=0:682327804 : : :) is the only real root of x + x − 1; we proceed to prove that whenever n ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2014
ISSN: 1077-8926
DOI: 10.37236/4412