{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:04:59Z","timestamp":1787321099584,"version":"build-2736575974"},"reference-count":13,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["J 3850-N32"],"award-info":[{"award-number":["J 3850-N32"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>It is known that the cop number $c(G)$ of a connected graph $G$ can be bounded as a function of the genus of the graph $g(G)$. The best known bound, that $c(G) \\leq \\left\\lfloor \\frac{3 g(G)}{2}\\right\\rfloor + 3$, was given by Schr\u00f6der, who conjectured that in fact $c(G) \\leq g(G) + 3$. We give the first improvement to Schr\u00f6der's bound, showing that $c(G) \\leq \\frac{4g(G)}{3} + \\frac{10}{3}$.<\/jats:p>","DOI":"10.1137\/20m1312150","type":"journal-article","created":{"date-parts":[[2021,10,19]],"date-time":"2021-10-19T10:50:34Z","timestamp":1634640634000},"page":"2459-2489","source":"Crossref","is-referenced-by-count":11,"title":["Bounding the Cop Number of a Graph by Its Genus"],"prefix":"10.1137","volume":"35","author":[{"given":"Nathan","family":"Bowler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joshua","family":"Erde","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Florian","family":"Lehner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Max","family":"Pitz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,10,19]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(84)90073-8"},{"key":"atypb2","first-page":"47","volume":"11","author":"Bonato A.","year":"2020","journal-title":"J. Comb."},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. Bonato and R. Nowakowski,\n                      The Game of Cops and Robbers on Graphs\n                      , Stud. Math. Libr. 61, American Mathematical Society, Providence, RI, 2011,https:\/\/doi.org\/10.1090\/stml\/061.","DOI":"10.1090\/stml\/061"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-012-1246-z"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2021.06.008"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20642"},{"key":"atypb7","unstructured":"B. Mohar,\n                      Notes on Cops and Robber Game on Graphs\n                      , preprint,https:\/\/arxiv.org\/abs\/1710.11281, 2017."},{"key":"atypb8","unstructured":"B. Mohar and C. Thomassen,\n                      Graphs on Surfaces\n                      , Johns Hopkins Stud. Math. Sci., Johns Hopkins University Press, Baltimore, MD, 2001."},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90160-7"},{"key":"atypb10","unstructured":"A. Quilliot,\n                      Jeux et pointes fixes sur les graphes\n                      , Ph.D. thesis, Universit\u00e9 de Paris VI, Paris, France, 1978."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(85)90093-0"},{"key":"atypb12","first-page":"243","author":"B. S.","year":"2001","journal-title":"Boston"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/100812963"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1312150","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:06:26Z","timestamp":1787317586000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1312150"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1312150"],"URL":"https:\/\/doi.org\/10.1137\/20m1312150","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}