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Graduate
By
Shiva Kintali
on Nov. 15, 2012 | Updated Dec. 6, 2017
Basics of Perfect Graphs
A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. Prove that bipartite graphs are perfect. Prove that the lin…
Mathematics
Graph Theory
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Graduate
By
Shiva Kintali
on June 7, 2012 | Updated Dec. 6, 2017
Recognizing series-parallel graphs in linear time
Let \(G(V,E)\) be a simple undirected graph with \(|V| = n\) and \(|E| = m\). Let the treewidth of \(G\) be at most \(k\). Derive a tight upper bound of \(m\) in terms of \(n\) and \(k\). Show that …
Computer Science
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chordal graph
linear time algorithms
series parallel
treewidth
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Graduate
By
Shiva Kintali
on June 8, 2012 | Updated Dec. 6, 2017
Simplicial vertices in Chordal graphs
Let \(G(V,E)\) be a simple undirected graph. Let \(v \in V\) and let \(N(v)\) denote the neighbors of \(v\) in \(G\). The vertex \(v\) is said to be simplicial if \(N(v)\) induces a clique in \(G\). …
Mathematics
Graph Theory
chordal graph
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