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Let ar(G,H) denote the maximum positive integer t, such that there is a t-edge-colored graph G without any rainbow subgraph H. We denote by kK2 a matching of size k and On the class of all maximal outer-planar graphs on n vertices, respectively. The outer-planar anti-Ramsey number of graph H, denoted by ar(On,H), is defined as max{ar(On,H)|On\u2208On}. It seems nontrivial to determine the exact values for ar(On,H) because most maximal outer-planar graphs are asymmetry. In this paper, we obtain that ar(On,kK2)\u2264n+3k\u22128 for all n\u22652k and k\u22656, which improves the existing upper bound for ar(On,kK2), and prove that ar(On,kK2)=n+2k\u22125 for n=2k and k\u22655. We also obtain that ar(On,6K2)=n+6 for all n\u226529.<\/jats:p>","DOI":"10.3390\/sym14061252","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T21:19:26Z","timestamp":1655673566000},"page":"1252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Outer-Planar Anti-Ramsey Number of Matchings"],"prefix":"10.3390","volume":"14","author":[{"given":"Changyuan","family":"Xiang","sequence":"first","affiliation":[{"name":"School of Science, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongxin","family":"Lan","sequence":"additional","affiliation":[{"name":"School of Science, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinghua","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Science, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changqing","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Hebei University of Technology, Tianjin 300401, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Bondy, J.A., and Murty, U.S.R. 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Matching Theory, Elsevier Science Publishers B.V.","DOI":"10.1016\/0044-8486(91)90002-O"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1252\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:32:52Z","timestamp":1760139172000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/6\/1252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,16]]},"references-count":25,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["sym14061252"],"URL":"https:\/\/doi.org\/10.3390\/sym14061252","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,16]]}}}