In graph theory, an st-planar graph is a bipolar orientation of a plane graph for which both the source and the sink of the orientation are on the outer face of the graph. That is, it is a directed graph drawn without crossings in the plane, in such a way that there are no directed cycles in the graph, exactly one graph vertex has no incoming edges, exactly one graph vertex has no outgoing edges, and these two special vertices both lie on the outer face of the graph. Within the drawing, each face of the graph must have the same structure: there is one vertex that acts as the source of the face, one vertex that acts as the sink of the face, and all edges within the face are directed along two paths from the source to the sink. If one draws an additional edge from the sink of an st-planar graph back to the source, through the outer face, and then constructs the dual graph (oriented each dual edge clockwise with respect to its primal edge) then the result is again an st-planar graph, augmented with an extra edge in the same way. (Wikipedia).
Planar graphs, What are planar graphs? In this video we take a look at what a planar graph is and how Mathematica can check to see if a graph is planar. In short, a planar graph is one that can be drawn in the plane such that no edges cross. If you want to learn more about Mathematica,
From playlist Introducing graph theory
Graph Theory: 57. Planar Graphs
A planar graph is a graph that can be drawn in the plane without any edge crossings. Such a drawing (with no edge crossings) is called a plane graph. A given plane graph divides the plane into regions and each region has a boundary that outlines it. We look at some examples and also giv
From playlist Graph Theory part-10
Planar 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
Introduction to Planar Graphs and Euler's Formula
This video introduces planar graphs and Euler's formula. http://mathispower4u.com
From playlist Graph Theory (Discrete Math)
What are Planar Graphs? | Graph Theory
What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t
From playlist Graph Theory
From playlist M. Graph Theory
Graph Theory: 59. Maximal Planar Graphs
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges. -- Bits of Graph Theory by Dr. Sarada Herke. Related videos: GT57 Planar G
From playlist Graph Theory part-10
Chandra Chekuri: On element connectivity preserving graph simplification
Chandra Chekuri: On element-connectivity preserving graph simplification The notion of element-connectivity has found several important applications in network design and routing problems. We focus on a reduction step that preserves the element-connectivity due to Hind and Oellerman which
From playlist HIM Lectures 2015
Regions In A Planar Graph - 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
Sally Dong: Nested Dissection Meets IPMs: Planar Min-Cost Flow in Nearly-Linear Time
We present a nearly-linear time algorithm for finding a minimum cost flow in planar graphs with polynomially bounded integer costs and capacities. Previously, the fastest algorithm for this problem was based on interior point methods (IPMs) and works for general sparse graphs in O(n^1.5 po
From playlist Workshop: Continuous approaches to discrete optimization
This video describes some of the basic properties of planar graphs.
From playlist Basics: Graph Theory
Rico Zenklusen: An O(1)-approximation for minimum spanning tree interdiction
Rico Zenklusen: An O(1)-approximation for minimum spanning tree interdiction Network interdiction studies the maximum impact that a removal of a limited number of edges or vertices can have on a graph optimization problem. Most interdiction problems are NP-hard, and only little is known a
From playlist HIM Lectures 2015
The Liouville conformal field theory quantum zipper - Morris Ang
Probability Seminar Topic: The Liouville conformal field theory quantum zipper Speaker: Morris Ang Affiliation: Columbia University Date: February 17, 2023 Sheffield showed that conformally welding a γ-Liouville quantum gravity (LQG) surface to itself gives a Schramm-Loewner evolution (
From playlist Mathematics
Planar Ising model at criticality: State-of-the-art and perspectives – Dmitry Chelkak – ICM2018
Analysis and Operator Algebras | Probability and Statistics Invited Lecture 8.7 | 12.8 Planar Ising model at criticality: State-of-the-art and perspectives Dmitry Chelkak Abstract: In this essay, we briefly discuss recent developments, started a decade ago in the seminal work of Smirnov
From playlist Probability and Statistics
Armand Riera: The scaling limit of random planar maps with large faces
HYBRID EVENT Recorded during the meeting "Random Geometry" the January 18, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Ahmad Abdi: Packing odd T-joins with at most two terminals
Ahmad Abdi: Packing odd T-joins with at most two terminals Let T be an even vertex subset, of size at most two, and let S be an edge subset of a graph. An edge subset is odd if it contains an odd number of edges of S. We are interested in packing edge-disjoint odd T-joins. The maximum siz
From playlist HIM Lectures 2015
Bertrand Eynard: (Mixed) topological recursion and the two-matrix model - Lecture 2
Mini course of the conference "Noncommutative geometry meets topological recursion", August 2021, University of Münster. Abstract: In this series of lecture we will introduce the 2-matrix model and the issue of mixed traces, then we shall give the answers as formulas. Some formulas will be
From playlist Noncommutative geometry meets topological recursion 2021
Vivek Madan: Simple and fast rounding algorithms for directed and node weighted multiway cut
Vivek Madan: Simple and fast rounding algorithms for directed and node-weighted multiway cut In the multiway cut problem, input is an edge/node weighted graph and a set of k terminals; the goal is to remove min-weight subset of edges/nodes such that there is no path between any two termin
From playlist HIM Lectures 2015
Planar 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