{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802444,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The Queen's Domination problem, studied for over 160 years, poses the following question: What is the least number of queens that can be arranged on a m \u00d7 n chessboard so that they either attack or occupy every cell? We propose a relaxation of the Queen's Domination problem and solve it exactly for rectangular chessboards. As a consequence, we improve on the best known lower bound for rectangular chessboards for one-eighth of the nontrivial cases. As another consequence, we generalize and provide a new interpretation of the best known lower bounds for Queen's Domination of square n \u00d7 n chessboards for n \u2261 {0, 1, 2} mod 4.Finally, we show some results and make some conjectures towards the goal of simplifying the long complicated proof for the best known lower bound for square boards when n \u2261 3 mod 4 (and n &gt; 11). These simply stated conjectures may also be of independent interest.<\/jats:p>","DOI":"10.37236\/12003","type":"journal-article","created":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T16:11:10Z","timestamp":1731687070000},"source":"Crossref","is-referenced-by-count":0,"title":["Improved Lower Bounds for Queen\u2019s Domination via an Exactly-Solvable Relaxation"],"prefix":"10.37236","volume":"31","author":[{"given":"Archit","family":"Karandikar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akashnil","family":"Dutta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,11,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p38\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p38\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T16:11:23Z","timestamp":1731687083000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p38"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,15]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12003","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,11,15]]},"article-number":"P4.38"}}