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The <jats:italic>weak rainbow saturation number<\/jats:italic> of , denoted by , is the minimum number of edges in a weakly \u2010rainbow saturated graph on  vertices. In this paper, we show that for any nonempty graph , the limit  exists. This answers a question of Behague et al. We also provide lower and upper bounds on this limit, and in particular, we show that this limit is nonzero if and only if  contains no pendant edges.<\/jats:p>","DOI":"10.1002\/jgt.23211","type":"journal-article","created":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T09:55:33Z","timestamp":1736157333000},"page":"35-42","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Weak Rainbow Saturation Numbers of Graphs"],"prefix":"10.1002","volume":"109","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7070-1174","authenticated-orcid":false,"given":"Xihe","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Shaanxi Normal University Xi'an Shaanxi China"},{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0095-255X","authenticated-orcid":false,"given":"Jie","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"},{"name":"Hefei National Laboratory University of Science and Technology of China Hefei Anhui China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tianying","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences University of Science and Technology of China Hefei Anhui China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,1,6]]},"reference":[{"key":"e_1_2_8_2_1","first-page":"163","article-title":"On Some Properties of Linear Complexes (In Russian)","volume":"24","author":"Zykov A. 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