On the complexity of the G-reconstruction problem

Authors:
Zdeněk Dvořák;Vít Jelínek
Affiliations:
Department of Applied Mathematics, Charles University, Praha 1;Department of Applied Mathematics, Charles University, Praha 1
Venue:
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Year:
2005

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Abstract

Let G be a fixed undirected graph. The G-structure of a graph F is the hypergraph H with the same set of vertices as F and with the property that a set h is a hyperedge of H if and only if the subgraph of F induced on h is isomorphic to G. For a fixed parameter graph G, we consider the complexity of determining whether for a given hypergraph H there exists a graph F such that H is the G-structure of F. It has been proven that this problem is polynomial if G is a path with at most 4 vertices ([9], [10]). We investigate this problem for larger graphs G and show that for some G the problem is NP-complete – in fact we prove that it is NP-complete for almost all graphs G.