Exercises
Multiple Choice
Articles
Open Problems
Login
10 items
Tagged:
lecture notes
x
bipartite graph
x
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
0
Undergraduate
By
diego
on June 27, 2012 | Updated Dec. 6, 2017
Unmatchable edges of bipartite graphs
Prove that the following algorithm finds the unmatchable edges of a bipartite graph \(G\) (edges that aren't in any perfect matching): find a perfect matching in \(G\), orient the unmatched edges from…
Mathematics
Graph Theory
bipartite graph
matching
0
Graduate
By
Shiva Kintali
on Sept. 11, 2012 | Updated Dec. 6, 2017
Vertex cover in bipartite graphs
The Vertex Cover of a graph \(G(V,E)\) is a set of vertices \(S \subseteq V\) such that each edge of the graph is incident to at least one vertex of the set \(S\). Minimum cost vertex cover : Given a…
Mathematics
Optimization
Graph Theory
Linear Programming
bipartite graph
vertex cover
0
Undergraduate
By
Shiva Kintali
on July 30, 2012 | Updated Dec. 6, 2017
k-regular bipartite graphs are 2-connected
Prove that every connected \(k\)-regular bipartite graph on at least three vertices is 2-connected.
Mathematics
Graph Theory
bipartite graph
connectivity
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Regular bipartite super-graph
Let \(G\) be a simple bipartite graph where each side of the bi-partition has size \(n\). The maximum degree of \(G\) is \(\Delta \le n/10\). Show that there exists a \(2 \Delta\)-regular simple bip…
Computer Science
Mathematics
Algorithms
Graph Theory
bipartite graph
graph algorithms
0
Graduate
By
Shiva Kintali
on Sept. 23, 2012 | Updated Dec. 6, 2017
Characterizing factor-critical graphs
A graph \(G\) is said to be factor-critical if \(G-v\) has perfect matching for every \(v \in V(G)\). Prove that no bipartite is factor-critical. Show that \(G\) is factor-critical if and only if …
Mathematics
Graph Theory
bipartite graph
matching
0
Undergraduate
By
Shiva Kintali
on May 21, 2013 | Updated Dec. 6, 2017
Covering complete graph with bipartite graphs
The union of graphs \(G_1, \dots, G_k\), written \(G_1 \cup \dots \cup G_k\), is the graph with vertex set \(V(G_1) \cup \dots \cup V(G_k)\) and edge set \(E(G_1) \cup \dots \cup E(G_k)\). Prove tha…
Mathematics
Graph Theory
bipartite graph
graph union
0
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
basics
bipartite graph
chordal graph
graph coloring
interval graph
perfect graphs
0
Undergraduate
By
Shiva Kintali
on June 17, 2012 | Updated Dec. 6, 2017
Matching saturating high degree vertices
Let \(G\) be a bipartite multigraph and let \(\Delta\) be its maximum degree. Prove that \(G\) has a matching saturating every vertex of degree \(\Delta\).
Mathematics
Graph Theory
bipartite graph
matching
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Lonely edges in bipartite graphs
Let \(G\) be an \(X,Y\)-bipartite graph with \(|X|=|Y|=n\). Suppose that \(G\) has a perfect matching. An edge in \(G\) is lonely if it belongs to no perfect matching. Prove that \(G\) has at most \…
Mathematics
Graph Theory
bipartite graph
matching
0
Undergraduate
By
Shiva Kintali
on May 22, 2013 | Updated Dec. 6, 2017
Basics of bipartite graphs
Prove the following properties of bipartite graphs : Prove that a graph \(G\) is bipartite if and only if every subgraph \(H\) of \(G\) has an independent set consisting of at least half of \(V(H)\)…
Mathematics
Graph Theory
basics
bipartite graph
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
bipartite graph
connectivity
pigeonhole principle
circumcircle
incircle
jee
jee 2016
jee advanced
jee mathematics
basics
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
×