Chromatic polynomials and logarithmic concavity
نویسندگان
چکیده
منابع مشابه
Expansions of Chromatic Polynomials and Log-concavity
In this paper we present several results and open problems about logconcavity properties of sequences associated with graph colorings. Five polynomials intimately related to the chromatic polynomial of a graph are introduced and their zeros, combinatorial and log-concavity properties are studied. Four of these polynomials have never been considered before in the literature and some yield new ex...
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In the main this paper introduces the concept of chromatic harmonic polynomials denoted, $H^chi(G,x)$ and chromatic harmonic indices denoted, $H^chi(G)$ of a graph $G$. The new concept is then applied to finding explicit formula for the minimum (maximum) chromatic harmonic polynomials and the minimum (maximum) chromatic harmonic index of certain graphs. It is also applied to split graphs and ce...
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We observe that for any logarithmically concave nite sequence a 0 , a 1 , : : : , a n of positive integers there is a representation of the Lie algebra sl 2 (C) from which this logarithmic concav-ity follows. Thus, in applying this strategy to prove logarithmic concavity, the only issue is to construct such a representation naturally from given combinatorial data. As an example, we do this when...
متن کاملChromatic polynomials of some nanostars
Let G be a simple graph and (G,) denotes the number of proper vertex colourings of G with at most colours, which is for a fixed graph G , a polynomial in , which is called the chromatic polynomial of G . Using the chromatic polynomial of some specific graphs, we obtain the chromatic polynomials of some nanostars.
متن کاملh-Vectors of matroids and logarithmic concavity
Article history: Received 11 November 2012 Accepted 4 November 2014 Available online 13 November 2014 Communicated by Ezra Miller MSC: 05B35 52C35
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1974
ISSN: 0095-8956
DOI: 10.1016/0095-8956(74)90071-9