{"title":"Refining a chain theorem from matroids to internally 4-connected graphs","authors":"Chanun Lewchalermvongs , Guoli Ding","doi":"10.1016/j.aam.2024.102802","DOIUrl":null,"url":null,"abstract":"<div><div>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 <span><span>[2]</span></span> 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.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0196885824001349","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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