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Graduate
By
Shiva Kintali
on Feb. 20, 2013 | Updated Jan. 16, 2017
Treewidth and Cliques
A tree decomposition of a graph \(G(V, E)\) is a pair \(\mathcal{D} = ({X_i\ |\ i \in I}, T(I, F))\) where \({X_i\ |\ i \in I}\) is a collection of subsets of \(V\) (called bags) and \(T(I, F)\) is a …
Mathematics
Graph Theory
treewidth
0
Graduate
By
Shiva Kintali
on June 11, 2012 | Updated Jan. 16, 2017
Embedding complete bipartite graphs
Let \(S\) be an orientable surface of genus \(g \geq 0\). Prove that for every \(g \geq 0\) there exists an integer \(t\) such that \(K_{3,t}\) cannot be drawn on \(S\) without any crossings. What is…
Mathematics
Graph Theory
graph embedding
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Graduate
By
Shiva Kintali
on June 6, 2012 | Updated Jan. 16, 2017
Algebraic dual of graphs
Let \(G\) be a connected graph. An algebraic dual of \(G\) is a graph \(G'\) such that \(G\) and \(G'\) have the same set of edges, any cycle of \(G\) is a cut of \(G'\), and any cut of \(G\) is a cyc…
Mathematics
Graph Theory
matroids
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Undergraduate
By
Shiva Kintali
on June 26, 2012 | Updated Jan. 16, 2017
Complete balanced binary trees are graceful
Label the vertices of a tree (with \(n\) vertices) with integers from \(1\) to \(n\). Now label each edge with the absolute difference of the labels of its incident vertices. The labeling is said to b…
Mathematics
Graph Theory
graph labeling
0
Undergraduate
By
JeffE
on June 7, 2012 | Updated Jan. 16, 2017
Maintaining fitstrings
Every non-negative integer can be represented as the sum of distinct positive Fibonacci numbers. (As a warmup exercise, prove this claim!) In other words, instead of a string of bits, we can represe…
Computer Science
Algorithms
amortized analysis
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