A simple solution to the two paths problem in planar graphs
Information Processing Letters
On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Finding $k$ Disjoint Paths in a Directed Planar Graph
SIAM Journal on Computing
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph
Journal of the ACM (JACM)
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
Node-Disjoint Paths on the Mesh and a New Trade-Off in VLSI Layout
SIAM Journal on Computing
The two disjoint path problem and wire routing design
Proceedings of the 17th Symposium of Research Institute of Electric Communication on Graph Theory and Algorithms
A very practical algorithm for the two-paths problem in 3-connected planar graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
A Linear Time Algorithm for Finding Three Edge-Disjoint Paths in Eulerian Networks
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
Linear time algorithms for two disjoint paths problems on directed acyclic graphs
Theoretical Computer Science
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Given distinct vertices s 1,s 2,t 1, and t 2 the 2-vertex-disjoint paths problem (2-VDPP) consists in determining two vertex-disjoint paths p 1, from s 1 to t 1, and p 2, from s 2 to t 2, if such paths exist. We show that by using some kind of sparsification technique the previously best known time bound of O(n + mα(m,n)) can be reduced to O(m + nα(n,n)), where α denotes the inverse of the Ackermann function. Moreover, we extend the very practical and simple algorithm of Hagerup for solving the 2-VDPP on 3-connected planar graphs to a simple linear time algorithm for the 2-VDPP on general planar graphs thereby avoiding the computation of planar embeddings or triconnected components.