Примеры использования Maximal planar на Английском языке и их переводы на Русский язык
{-}
-
Official
-
Colloquial
They are the maximal planar graphs with degeneracy three.
Therefore, strangulated graphs include maximal planar graphs.
Every maximal planar graph, other than K4 W4, contains as a subgraph either W5 or W6.
It ranges from 0 for trees to 1 for maximal planar graphs.
Every maximal planar graph with five or more vertices has vertex connectivity 3, 4, or 5.
Люди также переводят
The meshedness coefficient ranges between 0 for trees and 1 for maximal planar graphs.
Apollonian networks are chordal maximal planar graphs, or equivalently planar 3-trees.
However, there are infinitely many 3-connected well-covered maximal planar graphs.
In a maximal planar graph, the book thickness is two if and only if a Hamiltonian cycle exists.
When drawn on a plane, all its faces are triangular,making it a maximal planar graph.
For instance, a maximal planar graph has such an embedding if and only if it contains a Hamiltonian cycle.
They characterize these graphs as being the clique-sums of chordal graphs and maximal planar graphs.
A maximal planar graph is a planar graph in which all faces, even the outer face, are triangles.
The observation that every chordal polyhedral graph is maximal planar was stated explicitly by Gerlach 2004.
Another more complicated Apollonian network was used by Nishizeki(1980)to provide an example of a 1-tough non-Hamiltonian maximal planar graph.
They are the chordal maximal planar graphs, the chordal polyhedral graphs, and the planar 3-trees.
This follows from the fact that finding Hamiltonian cycles in maximal planar graphs is NP-complete.
More strongly, by the same argument, if a maximal planar graph has a cycle of length k, it has cycles of all smaller lengths.
It is named after A. Goldner and Frank Harary,who proved in 1975 that it was the smallest non-Hamiltonian maximal planar graph.
The equivalence of planar 3-trees and chordal maximal planar graphs was stated without proof by Patil 1986.
He then constructs a maximal planar graph G from the intersection graph of the circles, together with one additional vertex adjacent to all the circles on the boundary of the packing.
His work stressed the existence of a particular partition of the edges of a maximal planar graph into three trees known as a Schnyder wood.
They are the maximal planar graphs with treewidth three, a class of graphs that can be characterized by their forbidden minors or by their reducability under Y-Δ transforms.
This forms an alternative characterization of the Apollonian networks: they are exactly the chordal maximal planar graphs or equivalently the chordal polyhedral graphs.
Complementing the characterization of well-covered simple polyhedra in three dimensions, researchers have also considered the well-covered simplicial polyhedra, orequivalently the well-covered maximal planar graphs.
Structures closely related to non-separating ear decompositions of maximal planar graphs, called canonical orderings, are also a standard tool in graph drawing.
The order in which the vertices are added to create the network is therefore a degeneracy ordering, andthe Apollonian networks coincide with the 3-degenerate maximal planar graphs.
Apollonian networks may equivalently be defined as the planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes.
As Seymour& Weaver(1984) show, these are the only possible buildingblocks of strangulated graphs: the strangulated graphs are exactly the graphs that can be formed as clique-sums of complete graphs and maximal planar graphs.
For instance, a well-covered 3-connected maximal planar graph may be obtained via the clique cover construction from any 3t-vertex maximal planar graph in which there are t disjoint triangle faces by adding t new vertices, one within each of these faces.