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A closely related result, Wagner's theorem, characterizes the planar graphs by their minors in terms of the same two forbidden graphs and ,. Every Kuratowski subgraph is a special case of a minor of the same type, and while the reverse is not true, it is not difficult to find a Kuratowski subgraph (of one type or the other) from one of these ...
Pages in category "Theorems in graph theory" The following 54 pages are in this category, out of 54 total. ... Kőnig's theorem (graph theory) Kotzig's theorem ...
The theorem was discovered by Julius Petersen, a Danish mathematician. It is one of the first results ever discovered in the field of graph theory. The theorem appears first in the 1891 article "Die Theorie der regulären graphs". To prove the theorem, Petersen's fundamental idea was to 'colour' the edges of a trail or a path alternatively red ...
Forbidden graph characterizations may be used in algorithms for testing whether a graph belongs to a given family. In many cases, it is possible to test in polynomial time whether a given graph contains any of the members of the obstruction set, and therefore whether it belongs to the family defined by that obstruction set.
A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Since such graphs have a unique embedding (up to flipping and the choice of the external face), the next bigger graph, if still planar, must be a refinement of the former graph. This allows to reduce the planarity test to just testing for each step whether the next added edge has both ends in the external face of the current embedding.
In mathematical logic, monadic second-order logic (MSO) is the fragment of second-order logic where the second-order quantification is limited to quantification over sets. [1] It is particularly important in the logic of graphs , because of Courcelle's theorem , which provides algorithms for evaluating monadic second-order formulas over graphs ...
In the study of graph algorithms, Courcelle's theorem is the statement that every graph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth. [1] [2] [3] The result was first proved by Bruno Courcelle in 1990 [4] and independently rediscovered by Borie, Parker & Tovey (1992 ...