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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Dvořák, Z., Jelínek, V. (2005). On the Complexity of the G-Reconstruction Problem. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_21
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DOI: https://doi.org/10.1007/11602613_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
Online ISBN: 978-3-540-32426-3
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