Examples of using Complete graph in English and their translations into Hungarian
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For the complete graph Kn.
Such a graph is termed a complete graph.
We denote the complete graph with order n by K n.
Richard Guy showed(1972) that for complete graphs Kn.
The complete graph K m{\displaystyle K_{m}} is strongly regular for any m{\displaystyle m}.
So this gives us a complete graph.
Except for complete graphs, κ(G) equals the minimum of κ(u, v) over all nonadjacent pairs of vertices u, v.
For k= 2,the unique forbidden minor is the 4-vertex complete graph K4.
The problem is equivalent to determining whether the complete graph K9 is biplanar(it is not, and the conjecture is true).
This is equivalent to the condition that the inducedsubgraph of G induced by C is a complete graph.
Complete graphs are not included in this version of the definition since they cannot be disconnected by deleting vertices.
For a connected, simple graph G, unless G is a complete graph or an odd cycle.
The complete graph K6, the Petersen graph, and the other five graphs in the Petersen family do not have linkless embeddings.
In older mathematical terminology,the phrase"universal graph" was sometimes used to denote a complete graph.
It is known that it is possible to draw the complete graph with\(\displaystyle 7\) vertices on the surface of a torus(see the Császár polyhedron, for example).
This graph family may be characterized by a single forbidden minor,the four-vertex diamond graph formed by removing an edge from the complete graph K4.
According to Brooks' theorem every connected cubic graph other than the complete graph K4 can be colored with at most three colors.
However, the planar complete graph K4, and infinitely many other planar graphs containing K4, contain four triangles and are not 3-colorable.
Albertson in 2007, states that,among all graphs with chromatic number n, the complete graph Kn has the minimum number of crossings.
Nešetřil& Thomas(1985) observed that Sachs' question about the chromatic number would be resolved by a proof of Hadwiger's conjecture that anyk-chromatic graph has as a minor a k-vertex complete graph.
As shown in the first figure, the book thickness of the complete graph K5 is three: as a non-planar graph its book thickness is greater than two, but a book embedding with three pages exists.
The Albertson conjecture, formulated by Michael O. Albertson in 2007, states that,among all graphs with chromatic number n, the complete graph Kn has the minimum number of crossings.
Other open problems concerning the chromatic number of graphs include the Hadwiger conjecture stating that everygraph with chromatic number k has a complete graph on k vertices as a minor, the Erdős- Faber- Lovász conjecture bounding the chromatic number of unions of complete graphs that have at exactly one vertex in common to each pair, and the Albertson conjecture that among k-chromatic graphs the complete graphs are the ones with smallest crossing number.
The graphs with Hadwiger number at most five include the apex graphs and the linklessly embeddable graphs, both of which have the complete graph K6 among their forbidden minors.
Kuratowski's theorem that a graph is planar if and only if it does notcontain 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).
The Brooks's Law analysis(and the resulting fear of large numbers in development groups) rests on a hidden assumption:that the communications structure of the project is necessarily a complete graph, that everybody talks to everybody else.
As Seymour& Weaver(1984) show, these are the only possible building blocks of strangulatedgraphs: the strangulated graphs are exactly the graphs that can be formed as clique-sums of complete graphs and maximal planar graphs.
Graph measurement complete.
For instance a complete bipartite graph K1,n has the same line graph as the dipole graph and Shannon multigraph with the same number of edges.
Not every 2-vertex-connected graph is Hamiltonian;counterexamples include the Petersen graph and the complete bipartite graph K2,3.