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  2. Discharging method (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Discharging_method...

    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.

  3. Category:Theorems in graph theory - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_in_graph...

    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 ...

  4. List of theorems - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems

    De Bruijn–Erdős theorem (graph theory) De Finetti's theorem (probability) De Franchis theorem (Riemann surfaces) De Gua's theorem ; De Moivre's theorem (complex analysis) De Rham's theorem (differential topology) Deduction theorem ; Denjoy theorem (dynamical systems) Denjoy–Carleman theorem (functional analysis)

  5. Handshaking lemma - Wikipedia

    en.wikipedia.org/wiki/Handshaking_lemma

    In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. [ 1 ]

  6. Courcelle's theorem - Wikipedia

    en.wikipedia.org/wiki/Courcelle's_theorem

    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 ...

  7. 2-factor theorem - Wikipedia

    en.wikipedia.org/wiki/2-factor_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 ...

  8. Mac Lane's planarity criterion - Wikipedia

    en.wikipedia.org/wiki/Mac_Lane's_planarity_criterion

    In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who published it in 1937. It states that a finite undirected graph is planar if and only if the cycle space of the graph (taken modulo 2) has a cycle basis in which each edge of the graph ...

  9. Vizing's theorem - Wikipedia

    en.wikipedia.org/wiki/Vizing's_theorem

    In graph theory, Vizing's theorem states that every simple undirected graph may be edge colored using a number of colors that is at most one larger than the maximum degree Δ of the graph. At least Δ colors are always necessary, so the undirected graphs may be partitioned into two classes: "class one" graphs for which Δ colors suffice, and ...