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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 ...
The graph counting/removal lemma can be used to provide a quick and transparent proof of the Erdős–Stone theorem starting from Turán's theorem and to extend the result to Simonovits stability: for any graph and any >, there exists such that any -free graph on vertices with at least (()) edges can be transformed into a complete (())-partite ...
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 ...
These changes leave five bridges existing at the same sites that were involved in Euler's problem. In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but it must begin on one island and end on the other. [9]
We point out that Theorem 2 is an exact structure theorem since the precise structure of K 5-free graphs is determined. Such results are rare within graph theory. The graph structure theorem is not precise in this sense because, for most graphs H, the structural description of H-free graphs includes some graphs that are not H-free.
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently an acyclic undirected graph, or equivalently a disjoint union of trees. [2]
Here G is a graph, f is a function on graphs, e is any edge of G, G \ e denotes edge deletion, and G / e denotes contraction. Tutte refers to such a function as a W-function. [1] The formula is sometimes referred to as the fundamental reduction theorem. [2] In this article we abbreviate to DC.