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Undergraduate
By
Shiva Kintali
on Jan. 21, 2013 | Updated Jan. 16, 2017
Characterizing outerplanar graphs
A graph is outerplanar if it is isomorphic to a plane graph such that every vertex is incident with the unbounded face. Prove that a graph is outerplanar if and only if it has no subgraph isomorph…
Mathematics
Graph Theory
planar graphs
0
Undergraduate
By
JeffE
on June 6, 2012 | Updated Jan. 16, 2017
Longest increasing digital subsequence
Let \(S[1..n]\) be a sequence of integers between \(0\) and \(9\). A digital subsequence of \(S\) is a sequence \(D[1..k]\) of integers such that each integer \(D[i]\) is the numerical value of a sub…
Computer Science
Algorithms
dynamic programming
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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
0
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
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
0
Undergraduate
By
aa1062
on July 22, 2012 | Updated Jan. 16, 2017
Pecking order
A researcher is studying the social dynamics of chicken coops. In each coop, for each pair of chickens \(A\) and \(B\), there is a pecking relationship: either \(A\) pecks \(B\) or \(B\) pecks \(A\) (…
Mathematics
Graph Theory
tournament
0
Undergraduate
By
Jagadish
on Nov. 3, 2012 | Updated Jan. 16, 2017
Array to Histogram
Given an array A[1..n] containing integers between 1 to n, transform the array to contain counts of each number in their respective positions. Your algorithm should run in linear time and constant ext…
Computer Science
Algorithms
linear time algorithms
0
Undergraduate
By
TrueShelf Inc.
on Sept. 28, 2013 | Updated Jan. 16, 2017
Task assignment using Hall's Theorem
You are given a collection of tasks each of which must be assigned a time slot in the range {\(1,\dots,n\)}. Each task \(j\) has an associated interval \(I_j = [s_j,t_j]\) and the time slot assigned t…
Mathematics
Graph Theory
assignment
halls theorem
0
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
0
High School
By
Shiva Kintali
on June 21, 2012 | Updated Jan. 16, 2017
Togglers and Truthtellers
There are five people. Four of them are togglers, and the fifth person is a truthteller. A toggler tells either the truth or lie when you ask him a question. The second time you ask him a question…
Puzzles
Puzzles
logic puzzle
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