{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:07Z","timestamp":1787323027618,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100004735","name":"Hunan Provincial Natural Science Foundation of China","doi-asserted-by":"crossref","award":["2022JJ3002"],"award-info":[{"award-number":["2022JJ3002"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004735","name":"Hunan Provincial Natural Science Foundation of China","doi-asserted-by":"crossref","award":["2021JJ30169"],"award-info":[{"award-number":["2021JJ30169"]}],"id":[{"id":"10.13039\/501100004735","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271157"],"award-info":[{"award-number":["12271157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p>A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel [ J. Graph Theory, 99 (2022), pp. 217--230] proved that every 1-planar graph with minimum degree 3 and $n\\geq 7$ vertices has a matching of size at least $\\frac{n+12}{7}$, which is tight for some graphs. They also provided tight lower bounds for the sizes of matchings in 1-planar graphs with minimum degree 4 or 5. In this paper, we show that any 1-planar graph with minimum degree 6 and $n \\geq 36$ vertices has a matching of size at least $\\frac{3n+4}{7}$, and this lower bound is tight. Our result confirms a conjecture posed by Biedl and Wittnebel [ J. Graph Theory, 99 (2022), pp. 217--230].<\/jats:p>","DOI":"10.1137\/21m1459952","type":"journal-article","created":{"date-parts":[[2022,11,3]],"date-time":"2022-11-03T12:29:37Z","timestamp":1667478577000},"page":"2570-2584","source":"Crossref","is-referenced-by-count":3,"title":["On the Size of Matchings in 1-Planar Graph with High Minimum Degree"],"prefix":"10.1137","volume":"36","author":[{"given":"Yuanqiu","family":"Huang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1559-8909","authenticated-orcid":true,"given":"Zhangdong","family":"Ouyang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengming","family":"Dong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,11,3]]},"reference":[{"key":"atypb1","first-page":"258","volume":"247","author":"Berge C.","year":"1958","journal-title":"C. 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