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)||E(G)|) algorithm that constructs such a decomposition. In applications, the asymptotic performance can often be improved to O(|V (G)|). This decomposition will be used to find four independent spanning trees in a 4connected graph. Partially supported by NSF VIGRE grant Supported by CNPq (Proc: 200611/00-3) – Brazil. Partially supported by NSF grant DMS 9970527 and NSA grant MDA904-03-1-0052