Exercises
Multiple Choice
Articles
Open Problems
Login
7 items
Tagged:
treewidth
x
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
0
Graduate
By
Shiva Kintali
on June 10, 2012 | Updated Dec. 6, 2017
Basics of Treewidth
Treewidth of an undirected graph \(G\) measures how close \(G\) is to a tree. A tree decomposition of a graph \(G(V, E)\) is a pair \(\mathcal{D} = ({X_i\ |\ i \in I}, T(I, F))\) where …
Mathematics
Graph Theory
basics
treewidth
0
Graduate
By
Shiva Kintali
on June 7, 2012 | Updated Dec. 6, 2017
Recognizing series-parallel graphs in linear time
Let \(G(V,E)\) be a simple undirected graph with \(|V| = n\) and \(|E| = m\). Let the treewidth of \(G\) be at most \(k\). Derive a tight upper bound of \(m\) in terms of \(n\) and \(k\). Show that …
Computer Science
Mathematics
Algorithms
Graph Theory
chordal graph
linear time algorithms
series parallel
treewidth
0
Graduate
By
Shiva Kintali
on May 31, 2013 | Updated Dec. 6, 2017
Treewidth and circumference
Circumference of a graph is the length of its longest cycle. Prove that if a graph has circumference \(k\) then its treewidth is at most \(k-1\). Give a class of graphs showing that this bound is tigh…
Mathematics
Graph Theory
circumference
treewidth
0
Graduate
By
Shiva Kintali
on Feb. 20, 2013 | Updated Dec. 6, 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
diego
on Aug. 13, 2012 | Updated Dec. 6, 2017
Treewidth, the natural way
Given a graph \(G\), we define \(\mathrm{la}(G)\) as the smallest \(r\) such that \(G\) is a minor of some \(T\times K_r\), where \(T\) is a tree (and \(\times\) in this context is the cartesian produ…
Mathematics
Graph Theory
treewidth
0
Graduate
By
Shiva Kintali
on June 6, 2012 | Updated Dec. 6, 2017
Treewidth vs Pathwidth
Let \(G(V,E)\) be an undirected graph with \(|V|=n\) vertices. Let \(tw(G)\) and \(pw(G)\) represent the treewidth and pathwidth of \(G\) respectively. Let \(H\) be a tree. Prove that …
Mathematics
Graph Theory
pathwidth
treewidth
0
Graduate
By
Shiva Kintali
on June 4, 2013 | Updated Dec. 6, 2017
Treewidth and feedback vertex set
A feedback vertex set is a set of vertices whose removal results in an acyclic graph. Prove that if a graph has a feedback vertex set of size \(k\), then it has treewidth at most \(k+1\).
Mathematics
Graph Theory
treewidth
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
edge coloring
graph coloring
interview question
probability
pigeonhole principle
basics
connectivity
integration
jee
jee 2016
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
×