Dirac's theorem on simplicial matroids
组合数学
2007-10-14 v2 交换代数
摘要
We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the set [n] with a fixed k-skeleton. These simplicial complexes are a higher-dimensional analogue of clique (or flag) complexes (case k=2) and they are a rich new class of simplicial complexes. We show that Dirac's theorem on chordal graphs has a higher-dimensional analogue in which graphs and clique complexes get replaced, respectively, by simplicial matroids and k-hyperclique complexes. We prove also a higher-dimensional analogue of Stanley's reformulation of Dirac's theorem on chordal graphs.
引用
@article{arxiv.math/0609119,
title = {Dirac's theorem on simplicial matroids},
author = {Raul Cordovil and Manoel Lemos and Claudia Linhares Sales},
journal= {arXiv preprint arXiv:math/0609119},
year = {2007}
}
备注
11 pages; Annals of Combinatorics, to appear