{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:30:12Z","timestamp":1759638612359,"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>We prove that $\\lfloor{n+h\\over 4}\\rfloor$ vertex guards are always sufficient to see the entire interior of an $n$-vertex orthogonal polygon $P$ with an arbitrary number $h$ of holes provided that there exists a quadrilateralization whose dual graph is a cactus. Our proof is based upon $4$-coloring of a quadrilateralization graph, and it is similar to that of Kahn and others for orthogonal polygons without holes.  Consequently, we provide an alternate proof of Aggarwal's theorem asserting that $\\lfloor{n+h\\over 4}\\rfloor$ vertex guards always suffice to cover any $n$-vertex orthogonal polygon with $h \\le 2$ holes.<\/jats:p>","DOI":"10.37236\/1046","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:03:29Z","timestamp":1578719009000},"source":"Crossref","is-referenced-by-count":7,"title":["Orthogonal Art Galleries with Holes: A Coloring Proof of Aggarwal's Theorem"],"prefix":"10.37236","volume":"13","author":[{"given":"Pawe\u0142","family":"\u017byli\u0144ski","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,3,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:18:13Z","timestamp":1579321093000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1046","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2006,3,7]]},"article-number":"R20"}}