Random Arc Allocation and Applications
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Tail Bounds and Expectations for Random Arc Allocation and Applications
Combinatorics, Probability and Computing
A Simple Linear Time Algorithm for the Isomorphism Problem on Proper Circular-Arc Graphs
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Mutual exclusion scheduling with interval graphs or related classes, Part I
Discrete Applied Mathematics
| Hi-index | 0.00 |
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--403], 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 $O(n)$.