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.
|出版ステータス||出版済み - 2009|
|イベント||21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09 - Linz, オーストリア|
継続期間: 7 20 2009 → 7 24 2009
|その他||21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09|
|Period||7/20/09 → 7/24/09|
All Science Journal Classification (ASJC) codes