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Alexander duality and finite graphs

In: Monomial Ideals

Author

Listed:
  • Jürgen Herzog

    (Universität Duisburg-Essen, Fachbereich Mathematik)

  • Takayuki Hibi

    (Osaka University, Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology)

Abstract

Chapter 9 deals with the algebraic aspects of Dirac’s theorem on chordal graphs and the classification problem for Cohen–Macaulay graphs. First the classification of bipartite Cohen–Macaulay graphs is given. Then unmixed graphs are characterized and we present the result which says that a bipartite graph is sequentially Cohen–Macaulay if and only if it is shellable. It follows the classification of Cohen–Macaulay chordal graphs. Finally the relationship between the Hilbert–Burch theorem and Dirac’s theorem on chordal graphs is explained.

Suggested Citation

  • Jürgen Herzog & Takayuki Hibi, 2011. "Alexander duality and finite graphs," Springer Books, in: Monomial Ideals, chapter 9, pages 153-182, Springer.
    • Handle: RePEc:spr:sprchp:978-0-85729-106-6_9
    DOI: 10.1007/978-0-85729-106-6_9
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