{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:49:07Z","timestamp":1773150547201,"version":"3.50.1"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,12]]},"abstract":"<jats:p> We single out every longest path of n-1 order that solves each of the [Formula: see text] Longest Euclidean Hamiltonian Path Problems on the even nth root of the unity, by means of a geometric and arithmetic procedure. This identification is done regardless of planar rotations and orientation. In addition, the uniqueness of the Euclidean Hamiltonian cycle that resolves the Maximum Traveling Salesman Problem is shown. <\/jats:p>","DOI":"10.1142\/s1793830912500577","type":"journal-article","created":{"date-parts":[[2012,10,29]],"date-time":"2012-10-29T21:24:37Z","timestamp":1351545877000},"page":"1250057","source":"Crossref","is-referenced-by-count":3,"title":["EVERY LONGEST HAMILTONIAN PATH IN EVEN n-GONS"],"prefix":"10.1142","volume":"04","author":[{"given":"BLANCA I.","family":"NIEL","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad Nacional del Sur (UNS), Av. Alem 1253, Bah\u00eda Blanca (B8000CPB), Argentina"}]}],"member":"219","published-online":{"date-parts":[[2013,1,4]]},"reference":[{"key":"rf1","volume-title":"Traveling Salesman Problem: A Computational Study","author":"Applegate D.","year":"2006"},{"key":"rf2","volume-title":"Distance in Graphs","author":"Buckly F.","year":"1990"},{"key":"rf3","volume-title":"Introduction to Geometry","author":"Coxeter H. S. M.","year":"1963"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1145\/944618.944629"},{"key":"rf5","unstructured":"A.\u00a0Kirillov, Kvant Selecta: Algebra and Analysis, I (American Mathematical Society, 1999)\u00a0pp. 87\u201398."},{"key":"rf6","first-page":"47","volume":"78","author":"Niel B. I.","year":"2005","journal-title":"Model. Meas. Control A"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:14:32Z","timestamp":1565111672000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":6,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2013,1,4]]},"published-print":{"date-parts":[[2012,12]]}},"alternative-id":["10.1142\/S1793830912500577"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500577","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}