{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:44:11Z","timestamp":1759063451018},"reference-count":14,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,10,5]],"date-time":"2006-10-05T00:00:00Z","timestamp":1160006400000},"content-version":"vor","delay-in-days":5575,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1991,7]]},"abstract":"Abstract<\/jats:title>Let a<\/jats:italic> and b<\/jats:italic> be integers with b<\/jats:italic> \u2a7e a<\/jats:italic> \u2a7e 0. A graph G<\/jats:italic> is called an [a,b<\/jats:italic>]\u2010graph if a<\/jats:italic> \u2a7d d<\/jats:italic>G<\/jats:italic><\/jats:sub>(v<\/jats:italic>) \u2a7d b<\/jats:italic> for each vertex v<\/jats:italic> \u2208 V<\/jats:italic>(G<\/jats:italic>), and an [a,b<\/jats:italic>]\u2010factor of a graph G<\/jats:italic> is a spanning [a,b<\/jats:italic>]\u2010subgraph of G<\/jats:italic>. A graph is [a,b<\/jats:italic>]\u2010factorable if its edges can be decomposed into [a,b<\/jats:italic>]\u2010factors. The purpose of this paper is to prove the following three theorems: (i) if 1 \u2a7d b<\/jats:italic> \u2a7d 2a<\/jats:italic>, every [(12a<\/jats:italic> + 2)m<\/jats:italic> + 2an<\/jats:italic>,(12b<\/jats:italic> + 4)m<\/jats:italic> + 2bn<\/jats:italic>]\u2010graph is [2a<\/jats:italic>, 2b<\/jats:italic> + 1]\u2010factorable; (ii) if b<\/jats:italic> \u2a7d 2a<\/jats:italic> \u22121, every [(12a<\/jats:italic> \u22124)m<\/jats:italic> + 2an<\/jats:italic>, (12b<\/jats:italic> \u22122)m<\/jats:italic> + 2bn<\/jats:italic>]\u2010graph is [2a<\/jats:italic> \u22121,2b<\/jats:italic>]\u2010factorable; and (iii) if b<\/jats:italic> \u2a7d 2a<\/jats:italic> \u22121, every [(6a<\/jats:italic> \u22122)m<\/jats:italic> + 2an<\/jats:italic>, (6b<\/jats:italic> + 2)m<\/jats:italic> + 2bn<\/jats:italic>]\u2010graph is [2a<\/jats:italic> \u22121,2b<\/jats:italic> + 1]\u2010factorable, where m<\/jats:italic> and n<\/jats:italic> are nonnegative integers. They generalize some [a,b<\/jats:italic>]\u2010factorization results of Akiyama and Kano [3], Kano [6], and Era [5].<\/jats:p>","DOI":"10.1002\/jgt.3190150306","type":"journal-article","created":{"date-parts":[[2007,6,8]],"date-time":"2007-06-08T07:17:11Z","timestamp":1181287031000},"page":"283-301","source":"Crossref","is-referenced-by-count":9,"title":["[a,b<\/i>]\u2010factorizations of graphs"],"prefix":"10.1002","volume":"15","author":[{"given":"Cai","family":"Mao\u2010Cheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,5]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J.Akiyama Factorization and linear arboricity of graphs. Doctoral thesis Science University of Tokyo (1982)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090103"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090110"},{"key":"e_1_2_1_5_2","article-title":"A note on some factor theorems of graphs. Report No. 88526\u2010OR, Institut f\u00fcr \u00d6konometrie und Operations Research","author":"Mao\u2010cheng C.","year":"1988","journal-title":"Discrete Math."},{"key":"e_1_2_1_6_2","volume-title":"Graphs and Applications (Proceedings of the first Colorado Symposium on Graph Theory)","author":"Era H.","year":"1984"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190090111"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90077-8"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(70)80033-3"},{"key":"e_1_2_1_10_2","volume-title":"Matching Theory","author":"Lov\u00e1sz L.","year":"1985"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/1992894"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392606"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1952-028-2"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579180"},{"key":"e_1_2_1_15_2","volume-title":"Graph Theory","author":"Tutte W. T.","year":"1984"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190150306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190150306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T21:47:22Z","timestamp":1698011242000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190150306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,7]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,7]]}},"alternative-id":["10.1002\/jgt.3190150306"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190150306","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,7]]}}}