{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:44:00Z","timestamp":1759063440176,"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>Given a graph $G = (V,E)$, an even kernel is a nonempty independent subset $V' \\subseteq V$, such that every vertex of $G$ is adjacent to an even number (possibly 0) of  vertices in $V'$.  It is proved that the question of whether a graph has an even kernel is NP-complete.  The motivation  stems from combinatorial game theory.  It is known that this question is polynomial if $G$ is bipartite.  We also prove that  the question of whether there is an even kernel whose size is  between two given bounds, in a given bipartite graph, is NP-complete. This result has applications in coding and set theory.<\/jats:p>","DOI":"10.37236\/1185","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:41:02Z","timestamp":1578638462000},"source":"Crossref","is-referenced-by-count":4,"title":["Even Kernels"],"prefix":"10.37236","volume":"1","author":[{"given":"Aviezri","family":"Fraenkel","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1994,4,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v1i1r5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v1i1r5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:33:30Z","timestamp":1579340010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v1i1r5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,4,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1994,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/1185","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1994,4,13]]},"article-number":"R5"}}