{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:12Z","timestamp":1740155952880,"version":"3.37.3"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> Let [Formula: see text] be a finite set, and [Formula: see text] be a matroid defined on [Formula: see text]. Given [Formula: see text], we use the notations ([Formula: see text]-maximum bases packing for the first one): [Formula: see text] such that [Formula: see text] for any [Formula: see text], and [Formula: see text] for any basis [Formula: see text], and [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we give a short proof for the known min\u2013max relation [Formula: see text]. Moreover, we prove that the minimum [Formula: see text] can be restricted to single elements and semi locked subsets only. A subset [Formula: see text] is semi locked in [Formula: see text] if [Formula: see text] is closed and 2-connected, and [Formula: see text]. We deduce then a polynomial algorithm to compute [Formula: see text] in a large class of matroids by using a matroid oracle related to semi locked subsets. <\/jats:p>","DOI":"10.1142\/s1793830919500691","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T03:13:48Z","timestamp":1569554028000},"page":"1950069","source":"Crossref","is-referenced-by-count":0,"title":["A short proof of a min\u2013max relation for the bases packing of a matroid"],"prefix":"10.1142","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0689-6747","authenticated-orcid":false,"given":"Brahim","family":"Chaourar","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), P. O. Box 90950, Riyadh 11623, Saudi Arabia"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"S1793830919500691BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84628-970-5"},{"key":"S1793830919500691BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.2002.0604"},{"key":"S1793830919500691BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2007.05.007"},{"key":"S1793830919500691BIB004","doi-asserted-by":"publisher","DOI":"10.5402\/2011\/208478"},{"key":"S1793830919500691BIB006","doi-asserted-by":"publisher","DOI":"10.4236\/ojdm.2018.81002"},{"key":"S1793830919500691BIB007","doi-asserted-by":"publisher","DOI":"10.6028\/jres.069B.004"},{"issue":"4","key":"S1793830919500691BIB008","first-page":"437","volume":"62","author":"Feichtner E. M.","year":"2005","journal-title":"Port. Math."},{"key":"S1793830919500691BIB009","doi-asserted-by":"publisher","DOI":"10.15807\/jorsj.27.112"},{"key":"S1793830919500691BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-78240-4"},{"volume-title":"Matroid Theory","year":"1992","author":"Oxley J. G.","key":"S1793830919500691BIB011"},{"volume-title":"Combinatorial Optimization: Polyhedra and Efficiency","year":"2004","author":"Schrijver A.","key":"S1793830919500691BIB012"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500691","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T01:43:12Z","timestamp":1576806192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500691"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":11,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S1793830919500691"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500691","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}