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Journal Article

#### Detecting Directed 4-cycles Still Faster

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##### Citation

Eisenbrand, F., & Grandoni, F. (2003). Detecting Directed 4-cycles Still Faster.* Information Processing Letters,* *87*, 13-15.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-2CB8-3

##### Abstract

We present a method to detect simple cycles of length~4 of a
directed graph in~$O(n^{1/\omega} e^{2-2/\omega})$ steps, where
$n$~denotes the number of nodes, $e$ denotes the number of
edges and $\omega$ is the exponent of matrix multiplication. This
improves upon the currently fastest methods for
$\alpha\in (2/(4-\omega),(\omega+1)/2)$, where $e=n^\alpha$.