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Questions tagged [planar-graphs]

71 questions
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Planar regular languages

In my class a student asked whether all finite automata could be drawn without crossing edges (it seems all my examples did). Of course the answer is negative, the obvious automaton for the language $\{\; x\in\{a,b\}^* \mid \#_a(x)+2\#_b(x) \equiv 0…
Hendrik Jan
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Treewidth of k x k square grid graphs

According to some slides I found on google, the treewidth of any $k \times k$ square grid graph $G$ is $tw(G) = k$. I just started researching about treewidth and tree decomposition, and for the most part it makes sense. However, I am particularly…
saltthehash
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Why graph planarity is important

What is the reason to study planar graphs and algorithms on such graphs (as well as algorithms allowing to check a graph's planarity)? Where in industry this knowlege is needed? I know that planarity arises in microchip design ("wires"…
Stan
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Partitioning an undirected, unweighted, square planar graph paths that join certain pairs of nodes

I am trying to find a way to efficiently solve a puzzle that I play a lot by turning it into a graph partitioning problem (which is basically is in its actual form). I know that generally, graph partitioning problems are considered NP-hard or even…
saltthehash
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Algorithm to generate all planar graphs

Is there an algorithm which provides a sequence of all simple planar graphs, unique by graph isomorphism? For instance: first all planar graphs with 1 node, then all planar graphs with 2 nodes, etc. Note: It is okay if it generates only graphs with…
317070
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Subgraph isomorphism in planar graphs

I'm a computer engineer trying to understand this Eppstein paper for matching subgraphs in planar graphs. I'm trying to find subgraph matches to map an application graph (the subgraph) to a network-on-chip (the large graph). I have already…
mohsaied
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What edges are not in a Gabriel graph, yet in a Delauney graph?

It is know that the Gabriel graph of a point set $P \subset \mathbb{R}^2$, $\mathcal{GG}(P)$ is a subset of the corresponding Delauney graph $\mathcal{DG}(P)$, i.e. $\mathcal{GG}(P) \subseteq\mathcal{DG}(P)$. A Gabriel graph is defined as: The…
Wilhelm
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Converting a non-planar graph to planar

Suppose that we have a non-planar graph $G$ which is undirected and connected. Our aim is to remove a set of edges and/or a set of vertices and convert make $G$ planar while keeping the connectedness. Besides connectedness, $G$ is guaranteed to have…
padawan
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Near Triangulation Planar Graph

This is the problem I am dealing with: Given a set P of n points in general position, let a graph G be defined as follows: The vertex set is P. Two vertices, a and b, are joined by an edge provided there exists an axis parallel square S with a and…
Wonderful2019
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Simple proof that finding a combinatorial map of a planar graph given as an incidence matrix can be done in polynomial time?

Suppose that I have a graph $G = (V,E)$, given as an incidence matrix of edges and vertices. Suppose that $G$ is planar, that is, it can be embedded in the plane without edge crossings. I would like to construct in the combinatorial map…
Elle Najt
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Planarity testing given an embedding

I am given a connected graph $G$ with some embedding. I want to find a non-deterministic algorithm running in $O(n)$ time to decide whether $G$ with that embedding is a plane graph (i.e, can be drawn without intersecting edges). I know there exist…
nir shahar
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If a graph has $15$ vertices, one with degree $8$, $6$ with degree $6$, $8$ with degree $4$, is it a planar graph?

The question is as above. I want to prove that there exists a $K_5$ as a subgraph, so this graph is not a planar graph. But I failed. If you can help me, I will be very appreciative.
oyyko
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How to prove that the dual of the dual of a connected planar graph $G$ is isomorphic to $G$?

I find in many references the fact that if $G$ is a connected planar graph, then for any embedding, $G^{**} \cong G$. However, all those references either say that this fact is trivial, or give the proof as an exercice. I am ok that this is clear on…
Nathaniel
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Decomposing planar Hamiltonian graphs

I have the following the statement and I have to prove whether it is true or not. Given a planar and Hamiltonian graph $\mathbb{G} = (V, E)$, show that we can partition $E = E_1 \cup E_2 = E$ so that $G_1 = (V, E_1)$ and $G_2 = (V, E_2)$ are both…
Mohbenay
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How would I algorithmically "stretch" polygons on a plane by re-scaling the distances between interior points?

I've been thinking about a computational problem and could use some guidance for how to go about developing an algorithm to solve it. On a Euclidean plane, I have a polygon A, a set of points A* bounded by A, another polygon B (that does not…
Thuy Guevarra
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