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Questions tagged [planar-graph]

In graph theory, a planar graph is a graph that can be embedded in the plane without edge crossings.

In , a planar graph is a that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other.

Testing whether a graph is planar or not is called planarity testing. Kuratowski's theorem states that a graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (the utility graph, a complete bipartite graph on six vertices, three of which connect to each of the other three). Such a subgraph is called a Kuratowski subgraph. There are many algorithms to determine whether a certain graph is planar, one of the best known of which is the Boyer-Myrvold algorithm in O(n) (where n is the number of vertices).

Use this tag if you have questions about planarity testing implementations, libraries, or planar graph issues more generally.

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Weighted undirected graph partitioning

Given an undirected cyclic planar graph G(V,E) with vertex weights W(V), a fixed plane embedding E(G) and two nodes s and t, I need to find a partitioning of G that divides it into two connected components S(G) and T(G) with s being in S(G) and t…
Isolin
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Planar Embedding (Planar Face Traversal) Algorithm in C#

I have a graph G. The graph is a planar graph. I wish to find all the faces of the graph. I understand that constructing a planar embedding is the way to find the faces ( or regions, or cycles), such that all the edges must be shared by at most 2…
Graviton
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How to find the 'outline' of a (concave) graph in 2D plane?

I have a connected graph in 2D plane composed of some vertices and some edges defined between them. The overall shape of the graph is not necessarily convex, i.e. the adjacent vertices on the convex hull are not always connected by an edge. Now is…
Niko
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Python Library for Boyer-Myrvold planarity test or Kuratowski subgraph identification

I am working with NetworkX Graphs in Python and I would like to find the Kuratowski subgraphs of any given graph which I have. The Boyer-Myrvold planar graph testing algorithm can return an existing Kuratowski subgraph if the graph is not planar…
patapouf_ai
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Puzzle: Planar configuration of straight connecting lines

Puzzle : Given an even number of points in general positions on the plane (that is, no three points co-linear), can you partition the points into pairs and connect the two points of each pair with a single straight line such that the straight lines…
Dubby
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leftmost path in planar embedding

I have a directed planar Graph. Therefore I can make a planar embedding. I have to nodes s and t and I would like to find the leftmost path between s and t according to a specific embedding. Left is defined as David described in the comment. That…
Mark Token
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Planar graph from random points

I'm trying to create a graph with as many straight edges as possible between points without allowing any of the edges to intersect in Java. Basically, I'm trying to make a planar graph with a random amount of points. I somewhat understand how to…
John Smith
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Planar Graphs generation : The Euler's formula not always work?

I am trying to build some algorithm for planar graphs generation. I have read a lot of materials about this subject and here are some results: public Graph graph; ... public Level(int numPoints, int numEdges, int levelID, int timeLim) { …
user1697867
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A solution of problem related to planar graph

I need an approaching method theoretically to solve the below problem. (6pts.) For n ≥ 1 let Gn be the simple graph with vertex set V(Gn) = {1, 2, ..., n} in which two different vertices i and j are adjacent whenever j is a multiple of i or i is a…
Shaibal Saha
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Which algorithm should match this specific Graph

specific question here. Suppose you have a graph where each vertice specifies how many connections they must have to another vertices and the following rules/properties apply: 1- The graph can be incomplete (no need to every vertice to have a…
Francisco Azevedo
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