A survivable path \((W, P)\) between a pair of vertices \(x_i, x_j\) in an undirected simple graph \(G\) is an ordered pair of edge-disjoint simple paths consisting of a working path \(W = x_i, \ldots, x_j\) a protection path \(P = x_i, \ldots, x_j\).An optimal set of survivable paths in graph \(G\) corresponds to a set of mesh-restored lightpaths defined on an optical network that minimizes the number of used optical channels.In this paper, we present new properties of the working paths, which are contained in an optimal set of survivable paths in \(G\).
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