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Undergraduate
By Shiva Kintali on Oct. 3, 2013 | Updated Jan. 4, 2018

Minimum-weight spanning path

Let \(G\) be an undirected weighted complete graph. Iteratively select the edge of least weight such that the edges selected so far form a disjoint union of paths. After \(n-1\) steps, the result is a…
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Undergraduate
By Shiva Kintali on May 19, 2013 | Updated Dec. 6, 2017

Graphs with large min-degree

Let \(G\) be a graph in which every vertex has degree \(\geq 3\). Show that \(G\) contains a cycle of even length. Let \(G\) be a simple undirected graph in which every vertex has degree \(\ge k\). …
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