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arXiv · 2306.07514

Chordal matroids arising from generalized parallel connections

James Dylan Douthitt·James Oxley
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Abstract

A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors. We characterize the class by its forbidden induced minors; the case when $q=2$ is distinctive.

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James Dylan Douthitt, James Oxley. 2023-10-14. Chordal matroids arising from generalized parallel connections. https://doi.org/10.1016/j.aam.2023.102631

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