{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T05:01:26Z","timestamp":1764997286504,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Can the vertices of an arbitrary graph $G$ be partitioned into $A \\cup B$, so that $G[A]$ is a line-graph and $G[B]$ is a forest? Can $G$ be partitioned into a planar graph and a perfect graph? The NP-completeness of these problems are special cases of our result: if ${\\cal P}$ and ${\\cal Q}$ are additive induced-hereditary graph properties, then $({\\cal P}, {\\cal Q})$-colouring is NP-hard, with the sole exception of graph $2$-colouring (the case where both ${\\cal P}$ and ${\\cal Q}$ are the set ${\\cal O}$ of finite edgeless graphs). Moreover, $({\\cal P}, {\\cal Q})$-colouring is NP-complete iff ${\\cal P}$- and ${\\cal Q}$-recognition are both in NP.  This completes the proof of a conjecture of Kratochv\u00edl and Schiermeyer, various authors having already settled many sub-cases.<\/jats:p>","DOI":"10.37236\/1799","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:21:02Z","timestamp":1578720062000},"source":"Crossref","is-referenced-by-count":44,"title":["Vertex-Partitioning into Fixed Additive Induced-Hereditary Properties is  NP-hard"],"prefix":"10.37236","volume":"11","author":[{"given":"Alastair","family":"Farrugia","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:02:03Z","timestamp":1579323723000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,7,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1799","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,7,19]]},"article-number":"R46"}}