{"title":"Circuit Decompositions of Binary Matroids","authors":"Bryce Frederickson, Lukas Michel","doi":"10.1137/23m1587439","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1193-1201, June 2024. <br/> Abstract. Given a simple Eulerian binary matroid [math], what is the minimum number of disjoint circuits necessary to decompose [math]? We prove that [math] many circuits suffice if [math] is the complete binary matroid, for certain values of [math], and that [math] many circuits suffice for general [math]. We also determine the asymptotic behavior of the minimum number of circuits in an odd-cover of [math].","PeriodicalId":49530,"journal":{"name":"SIAM Journal on Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1587439","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1193-1201, June 2024. Abstract. Given a simple Eulerian binary matroid [math], what is the minimum number of disjoint circuits necessary to decompose [math]? We prove that [math] many circuits suffice if [math] is the complete binary matroid, for certain values of [math], and that [math] many circuits suffice for general [math]. We also determine the asymptotic behavior of the minimum number of circuits in an odd-cover of [math].
期刊介绍：
SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution.
Topics include but are not limited to:
properties of and extremal problems for discrete structures
combinatorial optimization, including approximation algorithms
algebraic and enumerative combinatorics
coding and information theory
additive, analytic combinatorics and number theory
combinatorial matrix theory and spectral graph theory
design and analysis of algorithms for discrete structures
discrete problems in computational complexity
discrete and computational geometry
discrete methods in computational biology, and bioinformatics
probabilistic methods and randomized algorithms.
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