Reconstruction of \((p, p+1)\)-graphs from elementary contractions (Q1196377)

Earlier workers had solved the problem of reconstruction of a simple graph \(G\) from the deck of its elementary contractions \(\{G_ e\mid e\in E\}\) in the cases where \(G\) is disconnected, a tree, a unicyclic graph, a cactus or a separable graph without end points. In this paper the author solves the problem when \(G\) is a \(p\)-point graph with \(p+1\) lines. The proof technique involves a preliminary result computing the number of triangles in \(G\) from a knowledge of the number of edges in the contractions \(G_ e\) (true for any simple \((p,q)\)-graph) and a case discussion based on the number of triangles of \(G\) (which is shown to be at most two).