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Reconstructing a Graph from its Neighborhood Lists

Published online by Cambridge University Press:  12 September 2008

Martin Aigner  and
Eberhard Triesch
Martin Aigner
Affiliation:
Freie Universität Berlin, Fachbereich Mathematik, WE 2, Arnimallee 3, 1000 Berlin 33, Germany
Eberhard Triesch
Affiliation:
Forschungsinsitut für Diskrete Mathematik, Nassestraße 2, 5300 Bonn 1, Germany
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Abstract

Associate to a finite labeled graph G(V, E) its multiset of neighborhoods (G) = {N(υ): υ ∈ V}. We discuss the question of when a list is realizable by a graph, and to what extent G is determined by (G). The main results are: the decision problem is NP-complete; for bipartite graphs the decision problem is polynomially equivalent to Graph Isomorphism; forests G are determined up to isomorphism by (G); and if G is connected bipartite and (H) = (G), then H is completely described.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 2 , June 1993 , pp. 103 - 113
Copyright
Copyright © Cambridge University Press 1993

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References

[1]Erdős, P. and Gallai, T. (1960) Graphs with prescribed degrees of vertices (Hungarian). Math. Lapok 11 264–274.Google Scholar
[2]Erdős, P., Jacobson, M.S. and Lehel, J. (1991) Graphs realizing the same degree sequences and their respective clique numbers. In: Alavi, et al. (eds.) Graph Theory, Combinatorics and Applications, John Wiley, 439–449.Google Scholar
[3]Hajnal, A. and Sós, V. (1978) Combinatorics. Coll. Math. Soc. J. Bolyai 18, North-Holland.Google Scholar
[4]Lubiw, A. (1981) Some NP-complete problems similar to graph isomorphism. SIAM J. Computing 10 11–21.CrossRefGoogle Scholar
[5]Köbler, J., Schöning, U. and Torán, J. (1993) The graph isomorphism problem. Progress in Theoretical Computer Science, Birkhäuser.Google Scholar