Takuro Abe ; Koji Nuida ; Yasuhide Numata - An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations

dmtcs:2754 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2754
An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their CharacterizationsArticle

Authors: Takuro Abe 1; Koji Nuida 2; Yasuhide Numata 3,4

  • 1 Department of Mathematics [Kyoto]
  • 2 Research Center for Information Security
  • 3 Department of Mathematical Informatics [Tokyo]
  • 4 Japan Science and Technology Agency

In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs, and show a characterization of those graphs. Moreover, we also describe a relation between signed graphs and a certain class of multiarrangements of hyperplanes, and show a characterization of free multiarrangements in that class in terms of the generalized chordal graphs, which generalizes a well-known result by Stanley on free hyperplane arrangements. Finally, we give a remark on a relation of our results with a recent conjecture by Athanasiadis on freeness characterization for another class of hyperplane arrangements.


Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)
Section: Proceedings
Published on: January 1, 2009
Imported on: January 31, 2017
Keywords: hyperplane arrangement,free arrangement,chordal graph,signed graph,characterization,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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