{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T05:13:36Z","timestamp":1736226816683,"version":"3.32.0"},"reference-count":37,"publisher":"EDP Sciences","issue":"1","license":[{"start":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T00:00:00Z","timestamp":1736121600000},"content-version":"vor","delay-in-days":5,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,12,6]]},"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>An odd [1, <jats:italic>b<\/jats:italic>]-factor of a graph <jats:italic>G<\/jats:italic> is a spanning subgraph <jats:italic>F<\/jats:italic> of <jats:italic>G<\/jats:italic> such that <jats:italic>d<jats:sub>F<\/jats:sub><\/jats:italic> (<jats:italic>u<\/jats:italic>) is odd and 1 \u2264 <jats:italic>d<jats:sub>F<\/jats:sub><\/jats:italic> (<jats:italic>u<\/jats:italic>) \u2264 <jats:italic>b<\/jats:italic> for every <jats:italic>u<\/jats:italic> <jats:italic>\u2208<\/jats:italic> <jats:italic>V<\/jats:italic> (<jats:italic>G<\/jats:italic>), where <jats:italic>b<\/jats:italic> is a positive odd integer. The matrix <jats:italic>Q<\/jats:italic>(<jats:italic>G<\/jats:italic>) = <jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>) + <jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>) is called the signless Laplacian matrix of <jats:italic>G<\/jats:italic>, where <jats:italic>D<\/jats:italic>(<jats:italic>G<\/jats:italic>) denotes the degree diagonal matrix of <jats:italic>G<\/jats:italic> and <jats:italic>A<\/jats:italic>(<jats:italic>G<\/jats:italic>) denotes the adjacency matrix of <jats:italic>G<\/jats:italic>. Let <jats:italic>q<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>G<\/jats:italic>) denote the signless Laplacian spectral radius of <jats:italic>G<\/jats:italic>. In this paper, we study the existence of an odd [1, <jats:italic>b<\/jats:italic>]-factor of a graph <jats:italic>G<\/jats:italic> and derive a signless Laplacian spectral radius condition for a graph to possess an odd [1, <jats:italic>b<\/jats:italic>]-factor.<\/jats:p>","DOI":"10.1051\/ro\/2024223","type":"journal-article","created":{"date-parts":[[2024,12,8]],"date-time":"2024-12-08T19:48:02Z","timestamp":1733687282000},"page":"33-41","source":"Crossref","is-referenced-by-count":0,"title":["An odd [1, <i>b<\/i>]-factor in a graph from signless Laplacian spectral radius"],"prefix":"10.1051","volume":"59","author":[{"given":"Sizhong","family":"Zhou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quanru","family":"Pan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/BF02582935","volume":"1","author":"Amahashi","year":"1985","journal-title":"Graphs Comb."},{"key":"R2","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/S0012-365X(01)00214-X","volume":"243","author":"Ando","year":"2002","journal-title":"Discrete Math."},{"key":"R3","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.laa.2004.08.014","volume":"395","author":"Brouwer","year":"2005","journal-title":"Linear Algebra App."},{"key":"R4","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/j.jctb.2008.06.008","volume":"99","author":"Cioab\u02c7a","year":"2009","journal-title":"J. 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