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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 ...
The discharging method is a technique used to prove lemmas in structural graph theory. [1] Discharging is most well known for its central role in the proof of the four color theorem. The discharging method is used to prove that every graph in a certain class contains some subgraph from a specified list.
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 ...
Ringel–Youngs theorem (graph theory) Robbins theorem (graph theory) Robertson–Seymour theorem (graph theory) Robin's theorem (number theory) Robinson's joint consistency theorem (mathematical logic) Rokhlin's theorem (geometric topology) Rolle's theorem ; Rosser's theorem (number theory) Rouché's theorem (complex analysis)
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 ...