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{{Short description|Planar bipartite graph with 25 vertices and 31 edges}} | properties = [[Bipartite graph|Bipartite]]<br>[[Planar graph|Planar]] ...

| properties = [[planar graph|Planar]]<br />[[unit distance graph|Unit distance]] ...ical]] field of [[graph theory]], the '''bull graph''' is a [[planar graph|planar]] [[undirected graph]] with 5 vertices and 5 edges, in the form of a triang ...

...graphs do not have longer cycles. More precisely, for any ordering of the graphs in <math>{\mathcal F}</math> into a sequence <math>G_0, G_1, \dots</math>, | title = Shortness exponents of families of graphs ...

* the family of 20 graphs generated from the [[complete graph]] <math>K_7</math>. * the family of 78 graphs generated from <math>K_7</math> and <math>K_{3,3,1,1}</math>. ...

...graph|Triangle-free]]<br>[[Polyhedral graph|Polyhedral]]<br>[[planar graph|Planar]] ...heorem]], it is a [[k-vertex-connected graph|3-vertex-connected]] simple [[planar graph]].<ref name=grun>[[Branko Grünbaum]], ''[[Convex Polytopes]]'', 2nd e ...

{{Short description|Planar, undirected graph with 2n vertices and 3n-2 edges}} ...aph|Unit distance]]<br>[[Hamiltonian graph|Hamiltonian]]<br>[[planar graph|Planar]]<br>[[Bipartite graph|Bipartite]] ...

...5.1312v3|title= Generic method for bijections between blossoming trees and planar maps|date=2015|class= math.CO}}</ref> ...e_slides>{{cite web|last1=Albenque|first1=Marie|title=Blossoming trees and planar maps|url=http://www.lix.polytechnique.fr/~albenque/slides/Albenque_IHP.pdf| ...

...most <math>k</math> concentric layers. The '''outerplanarity index''' of a planar graph is the minimum value of <math>k</math> for which it is <math>k</math> ...s on the unbounded (outside) face of the graph. A 2-outerplanar graph is a planar graph with the property that, when the vertices on the unbounded face are r ...

...]] field of [[graph theory]], the '''triangle graph''' is a [[planar graph|planar]] [[undirected graph]] with 3 vertices and 3 edges, in the form of a triang [[Category:Individual graphs]] ...

| image = [[File:Frucht planar Lombardi.svg|200px]] ...graph, the Frucht graph is [[polyhedral graph|polyhedral]] ([[planar graph|planar]] and [[k-vertex-connected graph|3-vertex-connected]]) and [[Hamiltonian g ...

| properties = [[Connected graph|connected]]<br>[[planar graph|planar]] [[Category:Parametric families of graphs]] ...

{{Short description|Abstraction of 2-colorable graphs}} ==Relation to bipartite graphs== ...

...ces. It ranges from 0 for [[Tree (graph theory)|trees]] to 1 for [[maximal planar graph]]s.<ref name=first> ...face cycles in the graph. This ratio is 0 for a tree and 1 for any maximal planar graph. ...

More generally, every planar graph of minimum degree at least three either has an edge of total degree a ...{2,n-2}</math> have edges with unbounded total degree. However, for planar graphs with vertices of degree lower than three, variants of the theorem have been ...

{{Short description|Planar graph with convex polygon faces}} In [[graph drawing]], a '''convex drawing''' of a [[planar graph]] is a drawing that represents the vertices of the graph as points in ...

| properties = [[Cubic graph|Cubic]]<br>[[Planar graph|Planar]]<br>[[Polyhedral graph|Polyhedral]] From a small planar graph called the Tutte fragment, [[W. T. Tutte]] constructed a non-Hamilton ...

...ncy of eight regions in the plane (lower left), or as the half-square of a planar bipartite graph (lower right, the graph of the [[rhombic dodecahedron]])]] ...raph theory)|clique]] connecting the corresponding vertices, unlike planar graphs in which the largest cliques have only four vertices.<ref name="cgp">{{cita ...

...of graphs with some regular structure, such as the [[Cartesian product of graphs|Cartesian product]] of a number of [[complete graph]]s.<ref name= weiss-lg> ...implies that the square grid graph is also a median graph. All square grid graphs are [[bipartite graph|bipartite]], which is easily verified by the fact tha ...

...lyhedral graphs are the [[k-vertex-connected graph|3-vertex-connected]], [[planar graph]]s. ...he polyhedron). It has no crossings, so every polyhedral graph is also a [[planar graph]]. Additionally, by [[Balinski's theorem]], it is a [[k-vertex-connec ...

| properties = [[polyhedral graph|Polyhedral]]<br/>[[planar graph|Planar]]<br/>[[Chordal graph|Chordal]]<br/>[[Perfect graph|Perfect]]<br/>[[Treewid ...tation|last1=Read|first1=R. C.|last2=Wilson|first2=R. J.|title=An Atlas of Graphs|location=Oxford, England|publisher=Oxford University Press|page=285|year=19 ...