# A linear-time algorithm to find a separator in a graph excluding a minor

@article{Reed2009ALA,
title={A linear-time algorithm to find a separator in a graph excluding a minor},
author={B. Reed and D. Wood},
journal={ACM Trans. Algorithms},
year={2009},
volume={5},
pages={39:1-39:16}
}
• Published 2009
• Mathematics, Computer Science
• ACM Trans. Algorithms
Let <i>G</i> be an <i>n</i>-vertex <i>m</i>-edge graph with weighted vertices. A pair of vertex sets <i>A</i>, <i>B</i> ⊆ <i>V</i>(<i>G</i>) is a 2/3<i>-separation</i> of <i>order</i> |<i>A</i> ∩ <i>B</i>| if <i>A</i> ∪ <i>B</i> = <i>V</i>(<i>G</i>), there is no edge between <i>A</i> − <i>B</i> and <i>B</i> − <i>A</i>, and both <i>A</i> − <i>B</i> and <i>B</i> − <i>A</i> have weight at most 2/3 the total weight of <i>G</i>. Let ℓ ∈ Z<sup>+</sup> be fixed. Alon et al.  presented an… Expand
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