{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T20:40:15Z","timestamp":1727469615579},"reference-count":0,"publisher":"Journal of Graph Algorithms and Applications","issue":"2","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JGAA"],"abstract":"We introduce and study the 1-planar packing problem: Given $k$ graphs with $n$ vertices $G_1, \\dots, G_k$, find a 1-planar graph that contains the given graphs as edge-disjoint spanning subgraphs. We mainly focus on the case when each $G_i$ is a tree and $k=3$. We prove that a triple consisting of three caterpillars or of two caterpillars and a path may not admit a 1-planar packing, while two paths and a special type of caterpillar always have one. We then study 1-planar packings with few crossings and prove that three paths (resp. cycles) admit a 1-planar packing with at most seven (resp. fourteen) crossings. We finally show that a quadruple consisting of three paths and a perfect matching with $n \\geq 12$ vertices admits a 1-planar packing, while such a packing does not exist if $n \\leq 10$.<\/jats:p>","DOI":"10.7155\/jgaa.00574","type":"journal-article","created":{"date-parts":[[2021,11,5]],"date-time":"2021-11-05T16:03:35Z","timestamp":1636128215000},"page":"605-624","source":"Crossref","is-referenced-by-count":2,"title":["Packing Trees into 1-planar Graphs"],"prefix":"10.7155","volume":"25","author":[{"given":"Felice","family":"De Luca","sequence":"first","affiliation":[]},{"given":"Emilio","family":"Di Giacomo","sequence":"additional","affiliation":[]},{"given":"Seok-Hee","family":"Hong","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Kobourov","sequence":"additional","affiliation":[]},{"given":"William","family":"Lenhart","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Liotta","sequence":"additional","affiliation":[]},{"given":"Henk","family":"Meijer","sequence":"additional","affiliation":[]},{"given":"Alessandra","family":"Tappini","sequence":"additional","affiliation":[]},{"given":"Stephen","family":"Wismath","sequence":"additional","affiliation":[]}],"member":"4175","published-online":{"date-parts":[[2021,11,1]]},"container-title":["Journal of Graph Algorithms and Applications"],"original-title":[],"link":[{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/paper574\/2378","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/download\/paper574\/2378","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,27]],"date-time":"2024-09-27T20:14:46Z","timestamp":1727468086000},"score":1,"resource":{"primary":{"URL":"https:\/\/jgaa.info\/index.php\/jgaa\/article\/view\/paper574"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,11,1]]}},"URL":"https:\/\/doi.org\/10.7155\/jgaa.00574","relation":{},"ISSN":["1526-1719"],"issn-type":[{"type":"electronic","value":"1526-1719"}],"subject":[],"published":{"date-parts":[[2021,11,1]]}}}