How is a Chordal Graph like a Supersolvable Binary Matroid?
Combinatorics
2007-05-23 v2
Abstract
Let G be a finite simple graph. From the pioneering work of R. P. Stanley it is known that the cycle matroid of G is supersolvable iff G is chordal (rigid): this is another way to read Dirac's theorem on chordal graphs. Chordal binary matroids are not in general supersolvable. Nevertheless we prove that, for every supersolvable binary matroid M, a maximal chain of modular flats of M canonically determines a chordal graph.
Keywords
Cite
@article{arxiv.math/0212099,
title = {How is a Chordal Graph like a Supersolvable Binary Matroid?},
author = {Raul Cordovil and David Forge and Sulamita Klein},
journal= {arXiv preprint arXiv:math/0212099},
year = {2007}
}
Comments
10 pages, 3 figures, to appear in Discrete Mathematics