Pushouts and Graph Reconstruction
Allen Parks · 1991
Reconstructibility of a graph G is shown to depend on the existence of morphisms that make each hypomorph of G a pushout of some card diagram G sub v approaches limit of N approaches limit of K, N a null graph and K a star graph. These morphisms i: N approaches limit of G sub v and j: N approaches limit of K are shown to exist for each hypomorph of G when there are isomorphisms psi, phi such that for some card G sub v, phi x i = i' x psi, i' a hypomorphically induced monomorphism. This result relates reconstructibility to certain symmetry properties of cards and subsumes the good neighbor theorems.