{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:41:04Z","timestamp":1753890064248,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Graph Theory","license":[{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:00:00Z","timestamp":1565136000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>Let $f:V\\rightarrow\\mathbb{Z}_k$ be a vertex labeling of a hypergraph $H=(V,E)$. This labeling induces an~edge labeling of $H$ defined by $f(e)=\\sum_{v\\in e}f(v)$, where the sum is taken modulo $k$. We say that $f$ is $k$-cordial if for all $a, b \\in \\mathbb{Z}_k$ the number of vertices with label $a$ differs by at most $1$ from the number of vertices with label $b$ and the analogous condition holds also for labels of edges. If $H$ admits a $k$-cordial labeling then $H$ is called $k$-cordial. The existence of $k$-cordial labelings has been investigated for graphs for decades. Hovey~(1991) conjectured that every tree $T$ is $k$-cordial for every $k\\ge 2$. Cichacz, G\\&amp;quot;orlich and Tuza~(2013) were first to investigate the analogous problem for hypertrees, that is, connected hypergraphs without cycles. The main results of their work are that every $k$-uniform hypertree is $k$-cordial for every $k\\ge 2$ and that every hypertree with $n$ or $m$ odd is $2$-cordial. Moreover, they conjectured that in fact all hypertrees are $2$-cordial. In this article, we confirm the conjecture of Cichacz et al. and make a step further by proving that for $k\\in\\{2,3\\}$ every hypertree is $k$-cordial.<\/jats:p><jats:p>Comment: 12 pages<\/jats:p>","DOI":"10.23638\/dmtcs-21-4-1","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:49:08Z","timestamp":1743698948000},"source":"Crossref","is-referenced-by-count":0,"title":["On cordial labeling of hypertrees"],"prefix":"10.23638","volume":"vol. 21 no. 4","author":[{"given":"Micha\u0142","family":"Tuczy\u0144ski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Przemys\u0142aw","family":"Wenus","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Krzysztof","family":"W\u0119sek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2019,8,7]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1711.06294v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1711.06294v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:49:09Z","timestamp":1743698949000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/4081"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,7]]},"references-count":0,"journal-issue":{"issue":"Graph Theory","published-online":{"date-parts":[[2019,8,7]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-21-4-1","relation":{"has-preprint":[{"id-type":"arxiv","id":"1711.06294v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1711.06294v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1711.06294","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1711.06294","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2019,8,7]]},"article-number":"4081"}}