Ad
related to: kuratowski's graph creator- Start Diagramming
Free 7-day trial with unlimited
documents and premium features.
- Hundreds Of Templates
Browse Through Our Diagram
Templates Gallery And Sign Up Now.
- Visio Import
Import and edit Visio files
online with Lucidchart.
- Pricing
Get Lucidchart starting
at $7.95/month.
- Lucidchart for Teams
Manage licenses, security and
documents with a team account.
- Buy Online
Save up to 20% with an
annual subscription.
- Start Diagramming
Search results
Results From The WOW.Com Content Network
Kuratowski's theorem states that a finite graph is planar if it is not possible to subdivide the edges of or ,, and then possibly add additional edges and vertices, to form a graph isomorphic to . Equivalently, a finite graph is planar if and only if it does not contain a subgraph that is homeomorphic to K 5 {\displaystyle K_{5}} or K 3 , 3 ...
A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph K 5 and the complete bipartite graph K 3,3. For Kuratowski's theorem, the notion of containment is that of ...
The Polish mathematician Kazimierz Kuratowski provided a characterization of planar graphs in terms of forbidden graphs, now known as Kuratowski's theorem: A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of the complete graph K 5 or the complete bipartite graph K 3,3 (utility graph).
Planarity testing algorithms typically take advantage of theorems in graph theory that characterize the set of planar graphs in terms that are independent of graph drawings. These include Kuratowski's theorem that a graph is planar if and only if it does not contain a subgraph that is a subdivision of K 5 (the complete graph on five vertices ...
Multiple proofs of this impossibility are known, and form part of the proof of Kuratowski's theorem characterizing planar graphs by two forbidden subgraphs, one of which is ,. The question of minimizing the number of crossings in drawings of complete bipartite graphs is known as Turán's brick factory problem , and for K 3 , 3 {\displaystyle K ...
The extremal number (,) is the maximum number of edges in an -vertex graph containing no subgraph isomorphic to . is the complete graph on vertices. (,) is the Turán graph: a complete -partite graph on vertices, with vertices distributed between parts as equally as possible.
Proof without words that a hypercube graph is non-planar using Kuratowski's or Wagner's theorems and finding either K 5 (top) or K 3,3 (bottom) subgraphs. Wagner published both theorems in 1937, [1] subsequent to the 1930 publication of Kuratowski's theorem, [2] according to which a graph is planar if and only if it does not contain as a subgraph a subdivision of one of the same two forbidden ...
The complete graph on n vertices is denoted by K n.Some sources claim that the letter K in this notation stands for the German word komplett, [4] but the German name for a complete graph, vollständiger Graph, does not contain the letter K, and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory.