Computing roots of graphs is hard
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 kth power of a graph is defined analogously. It has been conjectured that the problem of computing any square roo...
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| Published in | Discrete Applied Mathematics Vol. 54; no. 1; pp. 81 - 88 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
26.09.1994
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| Online Access | Get full text |
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| Summary: | 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
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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| ISSN: | 0166-218X 1872-6771 |
| DOI: | 10.1016/0166-218X(94)00023-9 |