Chordal matroids arising from generalized parallel connections II

Document Type

Article

Publication Date

3-1-2025

Abstract

In 1961, Dirac showed that chordal graphs are exactly the graphs that can be constructed from complete graphs by a sequence of clique-sums. In an earlier paper, by analogy with Dirac's result, we introduced the class of GF(q)-chordal matroids as those matroids that can be constructed from projective geometries over GF(q) by a sequence of generalized parallel connections across projective geometries over GF(q). Our main result showed that when q=2, such matroids have no induced minor in {M(C4),M(K4)}. In this paper, we show that the class of GF(2)-chordal matroids coincides with the class of binary matroids that have none of M(K4), M⁎(K3,3), or M(Cn) for n≥4 as a flat. We also show that GF(q)-chordal matroids can be characterized by an analogous result to Rose's 1970 characterization of chordal graphs as those that have a perfect elimination ordering of vertices.

Publication Source (Journal or Book title)

Advances in Applied Mathematics

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