{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T07:44:09Z","timestamp":1778917449713,"version":"3.51.4"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"20","license":[{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T00:00:00Z","timestamp":1722384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007059","name":"Univerzita Palack\u00e9ho v Olomouci","doi-asserted-by":"publisher","award":["PrF2024011"],"award-info":[{"award-number":["PrF2024011"]}],"id":[{"id":"10.13039\/501100007059","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005357","name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","doi-asserted-by":"publisher","award":["APVV-20-0069"],"award-info":[{"award-number":["APVV-20-0069"]}],"id":[{"id":"10.13039\/501100005357","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003194","name":"Agent\u00fara Ministerstva \u0160kolstva, Vedy, V\u00fdskumu a \u0160portu SR","doi-asserted-by":"publisher","award":["2\/0104\/24"],"award-info":[{"award-number":["2\/0104\/24"]}],"id":[{"id":"10.13039\/501100003194","id-type":"DOI","asserted-by":"publisher"}]},{"name":"OPII","award":["313011BWH2"],"award-info":[{"award-number":["313011BWH2"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is known that the so-called Beck\u2019s conjecture, i.e. the equality of the finite clique and chromatic numbers of a zero-divisor graph, holds for partially ordered sets Hala\u0161 and Jukl (Discrete Math 309(13):4584\u20134589, 2009). In this paper we present a simple direct proof of this fact. Also, the case when the finiteness assumption of the clique number is omitted is investigated. We have shown that the conjecture fails in general and a bunch of counterexamples is presented.<\/jats:p>","DOI":"10.1007\/s00500-024-09958-8","type":"journal-article","created":{"date-parts":[[2024,7,31]],"date-time":"2024-07-31T18:40:56Z","timestamp":1722451256000},"page":"12113-12118","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On zero-divisor graphs of infinite posets"],"prefix":"10.1007","volume":"28","author":[{"given":"Radom\u00edr","family":"Hala\u0161","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jozef","family":"P\u00f3cs","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,31]]},"reference":[{"key":"9958_CR1","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1006\/jabr.1993.1171","volume":"159","author":"DD Anderson","year":"1993","unstructured":"Anderson DD, Naseer M (1993) Beck\u2019s coloring of a commutative ring. 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