A linear algorithm for embedding planar graphs using PQ-trees
Journal of Computer and System Sciences
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Algorithms for the Minimum Edge Cover of H-Subgraphs of a Graph
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Topological morphing of planar graphs
Theoretical Computer Science
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The outerplanarity index of a planar graph G is the smallest k such that G has a k-outerplanar embedding. We show how to compute the outerplanarity index of an n-vertex planar graph in O(n2) time, improving the previous best bound of O(k3n2). Using simple variations of the computation we can determine the radius of a planar graph in O(n2) time and its depth in O(n3) time. We also give a linear-time 4-approximation algorithm for the outerplanarity index and show how it can be used to solve maximum independent set and several other NP-hard problems faster on planar graphs with outerplanarity index within a constant factor of their treewidth.