{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:55:21Z","timestamp":1758815721918,"version":"3.40.5"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T00:00:00Z","timestamp":1726617600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the list packing number of a graph, the least <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000191_inline1.png\"\/><jats:tex-math>\n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> such that there are always <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000191_inline2.png\"\/><jats:tex-math>\n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> disjoint proper list-colourings whenever we have lists all of size <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000191_inline3.png\"\/><jats:tex-math>\n$k$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> associated to the vertices. We are curious how the behaviour of the list packing number contrasts with that of the list chromatic number, particularly in the context of bounded degree graphs. The main question we pursue is whether every graph with maximum degree <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000191_inline4.png\"\/><jats:tex-math>\n$\\Delta$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has list packing number at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548324000191_inline5.png\"\/><jats:tex-math>\n$\\Delta +1$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Our results highlight the subtleties of list packing and the barriers to, for example, pursuing a Brooks\u2019-type theorem for the list packing number.<\/jats:p>","DOI":"10.1017\/s0963548324000191","type":"journal-article","created":{"date-parts":[[2024,9,18]],"date-time":"2024-09-18T08:16:36Z","timestamp":1726647396000},"page":"807-828","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["List packing number of bounded degree graphs"],"prefix":"10.1017","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2385-1137","authenticated-orcid":false,"given":"Stijn","family":"Cambie","sequence":"first","affiliation":[]},{"given":"Wouter","family":"Cames van Batenburg","sequence":"additional","affiliation":[]},{"given":"Ewan","family":"Davies","sequence":"additional","affiliation":[]},{"given":"Ross J.","family":"Kang","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,9,18]]},"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548324000191","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,11]],"date-time":"2024-11-11T13:25:00Z","timestamp":1731331500000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548324000191\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9,18]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2024,11]]}},"alternative-id":["S0963548324000191"],"URL":"https:\/\/doi.org\/10.1017\/s0963548324000191","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"type":"print","value":"0963-5483"},{"type":"electronic","value":"1469-2163"}],"subject":[],"published":{"date-parts":[[2024,9,18]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}