Graph invariants | Graph minor theory
In graph theory, the treewidth of an undirected graph is an integer number which specifies, informally, how far the graph is from being a tree. The smallest treewidth is 1; the graphs with treewidth 1 are exactly the trees and the forests. The graphs with treewidth at most 2 are the series–parallel graphs. The maximal graphs with treewidth exactly k are called k-trees, and the graphs with treewidth at most k are called partial k-trees. Many other well-studied graph families also have bounded treewidth. Treewidth may be formally defined in several equivalent ways: in terms of the size of the largest vertex set in a tree decomposition of the graph, in terms of the size of the largest clique in a chordal completion of the graph, in terms of the maximum order of a haven describing a strategy for a pursuit–evasion game on the graph, or in terms of the maximum order of a bramble, a collection of connected subgraphs that all touch each other. Treewidth is commonly used as a parameter in the parameterized complexity analysis of graph algorithms. Many algorithms that are NP-hard for general graphs, become easier when the treewidth is bounded by a constant. The concept of treewidth was originally introduced by Umberto Bertelè and Francesco Brioschi under the name of dimension. It was later rediscovered by Rudolf Halin, based on properties that it shares with a different graph parameter, the Hadwiger number. Later it was again rediscovered by Neil Robertson and Paul Seymour and has since been studied by many other authors. (Wikipedia).
Data structures: Introduction to Trees
See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described tree data structure as a logical model in computer science. We have briefly discussed tree as a non-linear hierarchical data structure, i
From playlist Data structures
Andreas E. Feldmann: A (1+ε)-embedding of low highway dimension graphs into bounded treewidth graphs
Andreas Emil Feldmann: A (1+ε)-embedding of low highway dimension graphs into bounded treewidth graphs Graphs with bounded highway dimension were introduced in [Abraham et al., SODA 2010] as a model of transportation networks. We show that any such graph can be embedded into a distributio
From playlist HIM Lectures 2015
Matthias Mnich: Approximating Sparsest Cut in Low-Treewidth Graphs
The fundamental sparsest cut problem takes as input a graph G together with the edge costs and demands, and seeks a cut that minimizes the ratio between the costs and demands across the cuts. For n-node graphs G of treewidth k, Chlamtáč, Krauthgamer, and Raghavendra (APPROX 2010) presented
From playlist Workshop: Approximation and Relaxation
Intro to Tree Graphs | Trees in Graph Theory, Equivalent Definitions
What are trees in graph theory? Tree graphs are connected graphs with no cycles. We'll introduce them and some equivalent definitions, with of course examples of tree graphs in today's graph theory video lesson! Some equivalent definitions of tree graphs are as follows. A graph is a tree
From playlist Graph Theory
Kristof Huszar: On the Pathwidth of Hyperbolic 3-Manifolds
Kristof Huszar, Inria Sophia Antipolis - Mediterranee, France Title: On the Pathwidth of Hyperbolic 3-Manifolds Abstract: In recent years there has been an emergence of fixed-parameter tractable (FPT) algorithms that efficiently solve hard problems for triangulated 3-manifolds as soon as t
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
This video introduces rooted trees and how to define the relationships among vertices in a rooted tree. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Graph Theory: 36. Definition of a Tree
In this video I define a tree and a forest in graph theory. I discuss the difference between labelled trees and non-isomorphic trees. I also show why every tree must have at least two leaves. An introduction to Graph Theory by Dr. Sarada Herke. Related Videos: http://youtu.be/zxu0dL436gI
From playlist Graph Theory part-7
Tree Graphs - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Polynomial Bounds for the Grid-Minor Theorem - Julia Chuzhoy
Polynomial Bounds for the Grid-Minor Theorem Julia Chuzhoy Toyota Technological Institute at Chicago February 10, 2014 One of the key results in Robertson and Seymour's seminal work on graph minors is the Grid-Minor Theorem (also known as the Excluded Grid Theorem). The theorem states that
From playlist Mathematics
We don't know what a tree is (and this video won't tell you)
Offset your carbon footprint with Wren! They'll protect 5 extra acres of rainforest for each of the first 100 people who sign up at https://www.wren.co/join/minuteearth. It turns out that defining what is and isn't a “tree” is way harder than it seems. LEARN MORE ************** To learn m
From playlist This Is Not A Playlist
Dominik Peters: Structural Tractability in Hedonic Games
Hedonic games are a well-studied model of coalition formation, in which selfish agents are partitioned into disjoint sets, and agents care about the make-up of the coalition they end up in. The computational problem of finding a stable outcome in a hedonic game tends to be computationally
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Introduction to Trees and Properties of Trees
This video introduces defines and gives the properties of tree graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Binary tree traversal - breadth-first and depth-first strategies
See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have discussed algorithms for binary tree traversal. We have talked about breadth-first and depth-first strategies for tree traversal like level-order, p
From playlist Data structures
Introduction to Spanning Trees
This video introduces spanning trees. mathispower4u.com
From playlist Graph Theory (Discrete Math)