A survey of the reconstruction conjecture
We begin by tracing the history of the Reconstruction Conjecture (RC) for graphs. After describing the RC as the problem of reconstructing a graph G from a given deck of cards, each containing just one point-deleted subgraph of G, we proceed to derive information about G which is deducible from this deck.
Various theorems proving the RC for trees are then taken up. The status of the RC for digraphs is reported. Several variations of the RC are stated and partial results obtained to date are indicated. We conclude with a summary of structures other than trees which have been reconstructed, and some remarks on the reconstruction of countably infinite graphs.
KeywordsCombinatorial Theory Reconstruction Problem Outerplanar Graph Unicyclic Graph Chromatic Polynomial
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