论文信息 - Computing Roots of Graphs Is Hard

Computing Roots of Graphs Is Hard

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.

Rajeev Motwani | Madhu Sudan

[1] T Rojano,et al. Characterization of n-path graphs and of graphs having nth root , 1974 .

[2] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3] Dennis P. Geller. The square root of a digraph , 1968 .

[4] A. Mukhopadhyay. The square root of a graph , 1967 .

[5] Nathan Linial,et al. Locality in Distributed Graph Algorithms , 1992, SIAM J. Comput..

[6] H. Fleischner. The square of every two-connected graph is Hamiltonian , 1974 .

[7] F. Harary,et al. The square of a tree , 1960 .

[8] W. T. Tutte,et al. A criterion for planarity of the square of a graph , 1967 .

[9] Hang Tong Lau. Finding a hamiltonian cycle in the square of a block , 1980 .

[10] Steven Skiena,et al. Algorithms for Square Roots of Graphs , 1991, SIAM J. Discret. Math..