Nonplanar topological inference and political-map graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Journal of the ACM (JACM)
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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
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GIS '03 Proceedings of the 11th ACM international symposium on Advances in geographic information systems
Recognizing string graphs in NP
Journal of Computer and System Sciences - STOC 2002
Journal of Computer and System Sciences - STOC 2001
Fixed-parameter algorithms for (k, r)-center in planar graphs and map graphs
ACM Transactions on Algorithms (TALG)
Fixed-parameter algorithms for the (k, r)-center in planar graphs and map graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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GD'04 Proceedings of the 12th international conference on Graph Drawing
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ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
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Chen, Grigni, and Papadimitriou (WADS'97 and STOC'98) have introduced a modified notion of planarity, where two faces are considered adjacent if they share at least one point. The corresponding abstract graphs are called map graphs. Chen et.al. raised the question of whether map graphs can be recognized in polynomial time. They showed that the decision problem is in NP and presented a polynomial time algorithm for the special case where we allow at most 4 faces to intersect in any point --- if only 3 are allowed to intersect in a point, we get the usual planar graphs.Chen et.al. conjectured that map graphs can be recognized in polynomial time, and in this paper, their conjecture is settled affirmatively.