کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6423592 1342425 2011 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The Hodge structure of the coloring complex of a hypergraph
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
The Hodge structure of the coloring complex of a hypergraph
چکیده انگلیسی

Let G be a simple graph with n vertices. The coloring complex Δ(G) was defined by Steingrímsson, and the homology of Δ(G) was shown to be nonzero only in dimension n−3 by Jonsson. Hanlon recently showed that the Eulerian idempotents provide a decomposition of the homology group Hn−3(Δ(G)) where the dimension of the jth component in the decomposition, Hn−3(j)(Δ(G)), equals the absolute value of the coefficient of λj in the chromatic polynomial of G, χG(λ).Let H be a hypergraph with n vertices. In this paper, we define the coloring complex of a hypergraph, Δ(H), and show that the coefficient of λj in χH(λ) gives the Euler Characteristic of the jth Hodge subcomplex of the Hodge decomposition of Δ(H). We also examine conditions on a hypergraph, H, for which its Hodge subcomplexes are Cohen-Macaulay, and thus where the absolute value of the coefficient of λj in χH(λ) equals the dimension of the jth Hodge piece of the Hodge decomposition of Δ(H). We also note that the Euler Characteristic of the jth Hodge subcomplex of the Hodge decomposition of the intersection of coloring complexes is given by the coefficient of jth term in the associated chromatic polynomial.

► We define the coloring complex of a hypergraph. ► A chromatic polynomial is related to the Euler Characteristic of the Hodge subcomplexes. ► We examine when the Hodge subcomplexes of the coloring complex are Cohen-Macaulay.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 311, Issue 20, 28 October 2011, Pages 2164-2173
نویسندگان
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