Cyclic coloring of plane graphs
Discrete Mathematics - Special volume (part 1) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs”
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient approximation schemes for maximization problems on K3,3-free of K5-free graphs
Journal of Algorithms
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Clique is hard to approximate within n1-
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
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This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+δ can be achieved in O(n2) time for any given constant δ 0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved in O(n7) time if no vertex is given a weight, while a ratio of O(log n) can be achieved in O(n7 log n) time otherwise. Behind the design of our algorithms are several fundamental results for map graphs; these results can be used to design good approximation algorithms for coloring and vertex cover in map graphs, and may find applications to other problems on map graphs as well.