Elsevier

Discrete Applied Mathematics

Volume 54, Issue 1, 26 September 1994, Pages 81-88
Discrete Applied Mathematics

Computing roots of graphs is hard

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Abstract

The square of an undirected graph G is the graph G2 on the same vertex set such that there is an edge between two vertices in G2 if and only if they are at distance at most 2 in G. The kth power of a graph is defined analogously. It has been conjectured that the problem of computing any square root of a square graph, or even that of deciding whether a graph is a square, is NP-hard. We settle this conjecture in the affirmative.

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1

Supported by Mitsubishi Corporation, NSF Grant CCR-9010517 and NSF Young Investigator Award CCR-9357849, with matching funds from IBM, Schlumberger Foundation, Shell Foundation, and Xerox Corporation.

2

Part of this research was done while this author was a student at the University of California at Berkeley, Supported by NSF PYI Grant CCR-8896202.