Chordal matroids arising from generalized parallel connections II

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-12-13 DOI:10.1016/j.aam.2024.102833

James Dylan Douthitt, James Oxley

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引用次数: 0

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

G F (q)

-chordal matroids as those matroids that can be constructed from projective geometries over

G F (q)

by a sequence of generalized parallel connections across projective geometries over

G F (q)

. Our main result showed that when

q = 2

, such matroids have no induced minor in

{M (C_{4}), M (K_{4})}

. In this paper, we show that the class of

G F (2)

-chordal matroids coincides with the class of binary matroids that have none of

M (K_{4})

M^{⁎} (K_{3, 3})

, or

M (C_{n})

for

n \geq 4

as a flat. We also show that

G F (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.

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来源期刊

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.