{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:30:13Z","timestamp":1753882213929,"version":"3.41.2"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071265"],"award-info":[{"award-number":["12071265"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271331"],"award-info":[{"award-number":["12271331"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["ZR202102250232"],"award-info":[{"award-number":["ZR202102250232"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> We consider a new coloring as follows such that a subset of [Formula: see text] needs very few colors. Let [Formula: see text] be a graph with vertex set [Formula: see text] and [Formula: see text] be three integers with [Formula: see text]. [Formula: see text] is a vertex subset of [Formula: see text], graph [Formula: see text] is said to be [Formula: see text]-weak [Formula: see text]-choosable about set [Formula: see text], if the following can be satisfied: For any list assignment [Formula: see text], there is a way that each vertex [Formula: see text] of [Formula: see text] is assigned [Formula: see text] colors of [Formula: see text] and each vertex [Formula: see text] of [Formula: see text] is assigned [Formula: see text] colors of [Formula: see text] such that the color sets corresponding to adjacent vertices do not intersect. In this paper, we consider the [Formula: see text]-weak [Formula: see text]-choosable problem of [Formula: see text]-planar graphs without short cycles and prove our results by the discharging method. In this paper, we prove that every [Formula: see text]-planar graph without [Formula: see text]-cycles, [Formula: see text]-cycles and adjacent [Formula: see text]-cycles is [Formula: see text]-weak [Formula: see text]-choosable about set [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830923501094","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T03:04:05Z","timestamp":1702350245000},"source":"Crossref","is-referenced-by-count":0,"title":["Fractional coloring problem of 1-planar graphs without short cycles"],"prefix":"10.1142","volume":"16","author":[{"given":"Meng Jiao","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, P. R. 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