Exercises
Multiple Choice
Articles
Open Problems
Login
Search
Sort By:
trending ▲
date
0
High School
By
Shiva Kintali
on Jan. 5, 2018
Evaluate Riemann Zeta function at all positive even integers
Reimann zeta function is the following \(\zeta(s) = \displaystyle\sum_{n=1}^{\infty}{\frac{1}{n^s}}\) Euler proved the following …
Mathematics
Mathematical Analysis
infinite series
riemann zeta function
0
Undergraduate
By
aa1062
on July 22, 2012 | Updated Dec. 6, 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
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Large min-degree implies perfect matching
Let \(G\) be a bipartite graph with partitions \(X\) and \(Y\) such that \(|X|=|Y|=n\). The degree of each vertex in \(G\) is at least \(n/2\). Prove that \(G\) has a perfect matching.
Mathematics
Graph Theory
matching
0
Undergraduate
By
Shiva Kintali
on June 7, 2012 | Updated Dec. 6, 2017
Number of edges in a quasi-planar graph
A graph \(G(V,E)\) is called quasi-planar if it can be drawn in the plane with no three pairwise crossing edges. Prove that a quasi-planar graph with \(|V| = n\) vertices has at most \(O(n^{3/2})\) ed…
Mathematics
Graph Theory
planar graphs
0
Undergraduate
By
Shiva Kintali
on July 17, 2012 | Updated Dec. 6, 2017
Number of triangles in a graph
Prove that a simple graph with \(n\) vertices and \(m\) edges has at least \(\frac{m}{3n}(4m − n^2)\) triangles.
Mathematics
Graph Theory
counting
0
Undergraduate
By
Shiva Kintali
on May 31, 2013 | Updated Dec. 6, 2017
Characterizations of Eulerian graphs
It is well-known that a graph is Eulerian if and only if every vertex has even degree. Prove the following alternate characterization of Eulerian graphs Prove that if \(G\) is Eulerian and …
Mathematics
Graph Theory
eulerian graph
0
Graduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 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
Undergraduate
By
True Putnam
on Aug. 28, 2013 | Updated Jan. 4, 2018
Putnam 2005 A6
Let \(n\) be given, \(n \geq 4\), and suppose that \(P_1,P_2, \dots,P_n\) are \(n\) randomly, independently and uniformly, chosen points on a circle. Consider the convex \(n\)-gon whose vertices are \…
Mathematics
Probability
uniform distribution
0
Graduate
By
Shiva Kintali
on June 11, 2012 | Updated Dec. 6, 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
High School
By
Shiva Kintali
on June 1, 2013 | Updated Dec. 6, 2017
The Sixth Sense
In the following, you are allowed to put any mathematical symbols on the left-hand side of the \("="\) sign to make the left-hand side evaluate to \(6\). For example, \(2+2+2=6\). Do this for all the …
Puzzles
Puzzles
math puzzle
1
2
3
...
24
25
26
next page »
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
trees
dynamic programming
polynomials
infinite series
digraphs
fermats little theorem
asymptotic analysis
differentiation
integration
jee
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×