How is a Chordal Graph like a Supersolvable Binary Matroid?

Details How is a Chordal Graph like a Supersolvable Binary Matroid? How is a Chordal Graph like a Supersolvable Binary Matroid?

2002-12-06

arxiv.org/abs/math/0212099v2

Mathematics

Combinatorics

10 pages, 3 figures, to appear in Discrete Mathematics

Scientific paper

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.

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