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In graph theory, a graph $G$ with edge set $E(G)$ is said to be $k$-edge-connected if $G\; setminus\; X$ is connected for all $X\; subseteq\; E(G)$ with $left|\; X\; right|\; <\; k$. In plain English, a graph is $k$-edge-connected if the graph remains connected when you delete fewer than $k$ edges from the graph.## See also

If a graph $G$ is $k$-edge-connected then $k\; le\; delta(G)$, where $delta(G)$ is the minimum degree of any vertex $v\; in\; V(G)$. This fact is clear since deleting all edges with an end at a vertex of minimum degree will disconnect that vertex from the graph.

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Last updated on Thursday May 01, 2008 at 14:16:26 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Thursday May 01, 2008 at 14:16:26 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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