{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:41Z","timestamp":1753893821530,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We show that two results on covering of edge colored graphs by monochromatic connected parts can be extended to partitioning. We prove that for any $2$-edge-colored non-trivial $r$-uniform hypergraph $H$, the vertex set can be partitioned into at most $\\alpha (H)-r+2$ monochromatic connected parts, where $\\alpha (H)$ is the maximum number of vertices that does not contain any edge. In particular, any $2$-edge-colored graph $G$ can be partitioned into $\\alpha(G)$ monochromatic connected parts, where $\\alpha (G)$ denotes the independence number of $G$. This extends K\u00f6nig's theorem, a special case of Ryser's conjecture.  Our second result is about Gallai-colorings, i.e. edge-colorings of graphs without $3$-edge-colored triangles. We show that for any Gallai-coloring of a graph $G$, the vertex set of $G$ can be partitioned into monochromatic connected parts, where the number of parts depends only on $\\alpha(G)$. This extends its cover-version proved earlier by Simonyi and two of the authors.<\/jats:p>","DOI":"10.37236\/2121","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:24:24Z","timestamp":1578713064000},"source":"Crossref","is-referenced-by-count":2,"title":["Partition of Graphs and Hypergraphs into Monochromatic Connected Parts"],"prefix":"10.37236","volume":"19","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":[[2012,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i3p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:31:23Z","timestamp":1579300283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i3p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/2121","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,8,30]]},"article-number":"P27"}}