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Abstract: The square of an undirected graph G is the graph G 2 on the same vertex set such that there is an edge between two vertices in G 2 if and only if they are at distance at most 2 in G. The k'th 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. 1. Introduction We consider the problem of deciding whether ... (Update)
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...same. However, in the latter case, the original graph is given. While it is easy to compute the power graph G k from G, Motwani and Sudan [10] showed that it is NP hard to compute the k th root G of a graph G k . All of the algorithm presented in this paper work without...
...(u; v) 2 E if and only if dT (u; v) k. If T exists then it is called a k root tree of G. 3 It is NP complete to recognize a graph power [5], but it is possible to determine if a graph has a k root tree, for any fixed k, in O(n 3 ) time, where n is the number of vertices in the...
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BibTeX entry: (Update)
R. Motwani, and M. Sudan. Computing Roots of Graphs is Hard. Discrete Applied Mathematics, 54(1994):81--88. http://citeseer.ist.psu.edu/motwani94computing.html More
@article{ motwani94computing,
author = "Motwani and Sudan",
title = "Computing Roots of Graphs is Hard",
journal = "DAMATH: Discrete Applied Mathematics and Combinatorial Operations Research and Computer Science",
volume = "54",
year = "1994",
url = "citeseer.ist.psu.edu/motwani94computing.html" }
Citations (may not include all citations):4212 Computers and Intractability -- A Guide to the Theory of NP-.. (context) - Garey, Johnson - 1979
33 Locality in distributed graph algorithms (context) - Linial - 1992
20 an ordering of the set of vertices of a connected graph (context) - Sekanina - 1960
13 Algorithms for Square Roots of Graphs - Lin, Skiena - 1991
12 The square of every two-connected graph is Hamiltonian (context) - Fleischner - 1974
3 Finding a Hamiltonian Cycle in the Square of a Block (context) - Lau - 1980
3 The square root of a graph (context) - Mukhopadhyay - 1967
2 The square root of a digraph (context) - Geller - 1968
2 path graphs and of graphs having n'th root (context) - Escalante, Montejano et al. - 1974
2 A criterion for planarity of the square of a graph (context) - Harary, Karp et al. - 1967
1 Bell System Technical Journal (context) - Ross, Harary et al. - 1960
The graph only includes citing articles where the year of publication is known.
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