完善从矩阵到内部 4 连接图的链式定理

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-11-06 DOI:10.1016/j.aam.2024.102802

Chanun Lewchalermvongs , Guoli Ding

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引用次数: 0

摘要

图论和矩阵理论相互关联，矩阵为概括和分析图的结构和独立性提供了一种方法。链定理是矩阵和图论中的重要工具，可以分析与图相关的矩阵结构。Chun、Mayhew 和 Oxley [2] 的一项重大贡献是建立了内部 4 连接二元矩阵的链定理，阐明了其中的操作。我们的研究在此基础上将矩阵结果具体化为内部 4 连接的图。我们研究的主要目标是将这个矩阵的链式定理完善为内部 4 连接图的链式定理，使对矩阵理论不太熟悉的人更容易理解。

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Refining a chain theorem from matroids to internally 4-connected graphs

Graph theory and matroid theory are interconnected with matroids providing a way to generalize and analyze the structural and independence properties within graphs. Chain theorems, vital tools in both matroid and graph theory, enable the analysis of matroid structures associated with graphs. In a significant contribution, Chun, Mayhew, and Oxley [2] established a chain theorem for internally 4-connected binary matroids, clarifying the operations involved. Our research builds upon this by specifying the matroid result to internally 4-connected graphs. The primary goal of our research is to refine this chain theorem for matroids into a chain theorem for internally 4-connected graphs, making it more accessible to individuals less acquainted with matroid theory.

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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.