In graph theory, a nested triangles graph with n vertices is a planar graph formed from a sequence of n/3 triangles, by connecting pairs of corresponding vertices on consecutive triangles in the sequence. It can also be formed geometrically, by gluing together n/3 − 1 triangular prisms on their triangular faces.
This graph, and graphs closely related to it, have been frequently used in graph drawing to prove lower bounds on the area requirements of various styles of drawings.
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identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such it...
interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the trivially perfect graphs. A graph has...
universal for outerplanar graphs. Planar graphs that can be partitioned into nested cycles, 2-outerplanar graphs and planar graphs of bounded pathwidth, have...
computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information...
unit of each other. Indifference graphs are also the intersection graphs of sets of unit intervals, or of properly nested intervals (intervals none of which...
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each...
solving NP-hard optimization problems on these graphs. Separator hierarchies may also be used in nested dissection, an efficient variant of Gaussian elimination...
computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there...
bound, a better way of creating an Eulerian graph is needed. By the triangle inequality, the best Eulerian graph must have the same cost as the best travelling...
anywhere on the page; Any graph may be enclosed by a simple closed curve called a cut or sep. A cut can be empty. Cuts can nest and concatenate at will...
called a triangle group. In the sphere there are three Möbius triangles plus one one-parameter family; in the plane there are three Möbius triangles, while...
finding as many triangles as possible among the vertices of a convex polygon, such that no two triangles that share a vertex have nested angles at that...
a graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid. This graph can also be constructed as the generalized Petersen graph G(10...
triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles...
polygon of our subdivision in triangles, and restrict our data structure to the case of subdivisions formed exclusively by triangles. Kirkpatrick gives a data...
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number...
In the mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using...
Triangular trade or triangle trade is trade between three ports or regions. Triangular trade usually evolves when a region has export commodities that...
Dejter I. J.; Franek F.; Mendelsohn E.; Rosa Alexander "Triangles in 2-factorizations", Journal of Graph Theory, 26 (1997) 83-94. Dejter I. J.; Franek F.; Rosa...
field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing...
rubber stopper to insert glass tubing. Cork borers usually come in a set of nested sizes along with a solid pin for pushing the removed cork (or rubber) out...
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