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Graduate
By
Shiva Kintali
on June 8, 2012 | Updated Jan. 16, 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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Undergraduate
By
Shiva Kintali
on June 25, 2012 | Updated Jan. 16, 2017
Separator number of a tree
Let \(T(V,E)\) be a tree with \(|V| = n\) vertices. Let \(W\) be a subset of \(V\). Prove that there is a vertex \(v \in V\) such that every component of \(T - v\) contains at most …
Computer Science
Mathematics
Algorithms
Graph Theory
trees
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Undergraduate
By
aa1062
on July 22, 2012 | Updated Jan. 16, 2017
Prisoners finding numbers
A prison contains \(n\) prisoners, labeled \(1, 2, 3, \dots, n\). One day the warden announces that he is going to set up a room with \(n\) drawers in it, labeled \(1, 2, 3, \dots, n\). He will then …
Puzzles
Puzzles
strategy
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Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Jan. 16, 2017
Basics of Hamiltonicity
Let \(G(V,E)\) be a simple graph with \(n\) vertices and minimum degree \(\delta\). Also, for every two vertices \(x, y \in V\), \(|N(x) \cup N(y)| + \delta \ge n + 10\). Prove that \(G\) has a Hami…
Mathematics
Graph Theory
basics
hamiltonian cycle
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Undergraduate
By
domotorp
on June 18, 2012 | Updated Jan. 16, 2017
Volley planning
Suppose there are n soldiers in a row who want to fire at the same time. Each of them has a constant memory and can only communicate with its neighbors, i.e. send message to left or right one and rece…
Puzzles
Puzzles
communication complexity
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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
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