{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841423,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For $r\\geq 2$, $\\alpha \\geq r-1$ and $k\\geq 1$, let $c(r,\\alpha ,k)$ be the smallest integer $c$ such that the vertex set of any non-trivial $r$-uniform $k$-edge-colored hypergraph ${\\cal H}$ with $\\alpha ({\\cal H})=\\alpha$ can be covered by $c$ monochromatic connected components. Here $\\alpha({\\cal{H}})$ is the maximum cardinality of a subset $A$ of vertices in $\\cal{H}$ such that $A$ does not contain any edges. An old conjecture of Ryser is equivalent to $c(2,\\alpha,k)=\\alpha (r-1)$ and a recent result of Z. Kir\u00e1ly states that $c(r,r-1,k)=\\lceil \\frac{k}{r}\\rceil$ for any $r\\ge 3$.Here we make the first step to treat non-complete hypergraphs, showing that $c(r,r,r)=2$ for $r\\ge 2$ and $c(r,r,r+1)=3$ for $r\\ge 3$.<\/jats:p>","DOI":"10.37236\/4137","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T20:04:35Z","timestamp":1578686675000},"source":"Crossref","is-referenced-by-count":2,"title":["A Note on Covering Edge Colored Hypergraphs by Monochromatic Components"],"prefix":"10.37236","volume":"21","author":[{"given":"Shinya","family":"Fujita","sequence":"first","affiliation":[]},{"given":"Michitaka","family":"Furuya","sequence":"additional","affiliation":[]},{"given":"Andr\u00e1s","family":"Gy\u00e1rf\u00e1s","sequence":"additional","affiliation":[]},{"given":"\u00c1gnes","family":"T\u00f3th","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,5,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i2p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:59:13Z","timestamp":1579240753000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i2p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,13]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2014,3,31]]}},"URL":"https:\/\/doi.org\/10.37236\/4137","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,5,13]]},"article-number":"P2.33"}}