{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T08:47:20Z","timestamp":1787388440025,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[1996,5]]},"abstract":"<jats:p>We present an $O(n)$algorithm to find a maximum clique in a proper circular arc graph. We assume that the input graph is represented by a sorted simple family of circular arcs or by an equivalent representation. In Deng, Hell, and Huang [SIAM J. Comput., 25 (1996), pp. 390\u2013403], we gave an $O(m + n)$ algorithm to find such a representation for a proper circular arc graph given by its adjacency lists. As an application we also give an $O(n)$ algorithm for q-coloring proper circular arc graphs for a fixed q. (Such an algorithm was first given by Teng and Tucker.) Finally we indicate how our algorithm can be modified to find a maximum weight clique in a weighted graph, also in time $O(n)$.<\/jats:p>","DOI":"10.1137\/s0895480192242754","type":"journal-article","created":{"date-parts":[[2005,2,23]],"date-time":"2005-02-23T08:08:45Z","timestamp":1109146125000},"page":"274-289","source":"Crossref","is-referenced-by-count":13,"title":["A Linear Algorithm for Maximum Weight Cliques in Proper Circular Arc Graphs"],"prefix":"10.1137","volume":"9","author":[{"given":"Binay","family":"Bhattacharya","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pavol","family":"Hell","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,12]]},"reference":[{"key":"R1","unstructured":"B. Bhattacharya, D. M. Kaller, An O(m+nlogn) Algorithm for the Maximum Clique Problem in Circular Arc Graphs, Smon Fraser University report CSS\/LCCR TR 94-26"},{"key":"R2","unstructured":"X. Deng, P. Hell, J. Huang, E.  Balas, G.  Cornu\u00e9jols, R.  Kannan, Recognition and representation of proper circular arc graphs, Integer Programming and Combinatorial Optimization, Pittsburgh, PA, 1992, 114\u2013121, Proc. 2nd IPCO conference"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539792269095"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230040407"},{"key":"R5","volume-title":"Algorithmic graph theory and perfect graphs","author":"Golumbic Martin Charles","year":"1980"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-52921-7_59"},{"key":"R7","unstructured":"P. Hell, J. Huang, Linear Algorithms for c-Coloring and for Finding Maximum Cliques in Proper Circular Arc Graphs, 1993, Dept. of Math. and Compt. 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