{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T03:58:36Z","timestamp":1763092716255,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Graph and Algorithms","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Graphs and Algorithms<\/jats:p>\n          <jats:p xml:lang=\"en\">Let us assign positive integers to the edges and vertices of a simple graph G. As a result we obtain a vertex-colouring of G with integers, where a vertex colour is simply a sum of the weight assigned to the vertex itself and the weights of its incident edges. Can we obtain a proper colouring using only weights 1 and 2 for an arbitrary G? We give a positive answer when G is a 3-colourable, complete or 4-regular graph. We also show that it is enough to C use weights from 1 to 11, as well as from 1 to 11 [chi(G)\/2] + 1, for an arbitrary graph G.<\/jats:p>","DOI":"10.46298\/dmtcs.491","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T21:46:31Z","timestamp":1629755191000},"source":"Crossref","is-referenced-by-count":2,"title":["On a 1, 2 Conjecture"],"prefix":"10.46298","volume":"Vol. 12 no. 1","author":[{"given":"Jakub","family":"Przybylo","sequence":"first","affiliation":[{"name":"AGH University of Science and Technology [Krakow, PL]"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mariusz","family":"Wo\u017aniaK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2010,1,1]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dmtcs.episciences.org\/491\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dmtcs.episciences.org\/491\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:05:05Z","timestamp":1687291505000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/dmtcs.episciences.org\/491"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,1]]},"references-count":0,"journal-issue":{"issue":"Graph and Algorithms","published-online":{"date-parts":[[2010,1,1]]}},"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.46298\/dmtcs.491","relation":{"is-same-as":[{"id-type":"uri","id":"https:\/\/2.zoppoz.workers.dev:443\/https\/hal.science\/hal-00990444v1","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2010,1,1]]},"article-number":"491"}}