Graph reconstruction from path correlation data

Reconstruction of the Path Graph

Let P be a set of n ≥ 5 points in convex position in the plane. The path graph G(P ) of P is an abstract graph whose vertices are non-crossing spanning paths of P , such that two paths are adjacent if one can be obtained from the other by deleting an edge and adding another edge. We prove that the automorphism group of G(P ) is isomorphic to Dn, the dihedral group of order 2n. The heart of the ...

Image Reconstruction from Incomplete Data

Image Reconstruction from Incomplete Data

image reconstruction from incomplete data

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Graph reconstruction from subgraphs

The Reconstruction Conjecture asserts that every ÿnite simple undirected graph on 3 or more vertices is determined, up to isomorphism, by its collection of (unlabeled) one-vertex-deleted subgraphs. A more general problem can be investigated if the collection consists of all (unla-beled) subgraphs with a restricted number of vertices. Kelly (Paciÿc J. Math. 7 (1957) 961–968) ÿrst raised the poss...