由广义平行连接产生的弦拟阵

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2023-10-23 DOI:10.1016/j.aam.2023.102631

James Dylan Douthitt, James Oxley

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引用次数: 0

摘要

如果每一个长度至少为四的循环都有一个弦，那么图就是弦图。1961年，狄拉克将弦图描述为可以通过重复团和从完整图构建的图。推广这一点，我们考虑了一类简单的GF（q）-可表示拟阵，它可以通过在投影几何上的重复广义平行连接从GF（q）上的投影几何建立。我们证明了这类拟阵在诱导未成年人下是封闭的。我们以其被禁止诱导的未成年人来描述这个阶级；当q＝2时的情况是不同的。

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Chordal matroids arising from generalized parallel connections

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 $G F (q)$ -representable matroids that can be built from projective geometries over $G F (q)$ 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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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.