Chain Decompositions of 4-Connected Graphs

In this paper we give a decomposition of a $4$-connected graph $G$ into nonseparating chains, which is similar to an ear decomposition of a $2$-connected graph. We also give an $O(|V(G)|^2|E(G)|)$ algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to $O(|V(G)|^3)$. This decomposition will be used to find four independent spanning trees in a $4$-connected graph.

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