The Hamiltonian cycle problem is linear-time solvable for 4-connected planar graphs
Journal of Algorithms
A Polynomial Solution to the Undirected Two Paths Problem
Journal of the ACM (JACM)
A new look at fault tolerant network routing
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
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This work was motivated by the study of a multitree approach to reliability in distributed networks and by the study of non-separating paths and cycles in highly connected graphs. We first give a result on "non-separating chains" in 4-connected graphs. This result is then used to obtain a "non-separating chain decomposition" of a 4-connected graph G, and an O(|V(G)|2|E(G)|) algorithm for constructing such a decomposition. As an application of this decomposition, we show how to produce four "independent spanning trees" in a 4-connected graph in O(|V(G)|3) time.