Dirac's theorem on chordal graphs and Alexander duality

Authors:
Jürgen Herzog;Takayuki Hibi;Xinxian Zheng
Affiliations:
Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, 45117 Essen, Germany;Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan;Fachbereich Mathematik und Informatik, Universität Duisburg-Essen, 45117 Essen, Germany
Venue:
European Journal of Combinatorics
Year:
2004

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Cohen-Macaulay chordal graphs

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Stanley decompositions and partitionable simplicial complexes

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Monomial ideals, edge ideals of hypergraphs, and their graded Betti numbers

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Shellable graphs and sequentially Cohen--Macaulay bipartite graphs

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Note: Ideals with linear quotients

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Enumeration of the perfect sequences of a chordal graph

Theoretical Computer Science

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Abstract

By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs and some algebraic applications.