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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 ...
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points ) which are connected by edges (also called arcs , links or lines ).
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.
Gödel's second incompleteness theorem; Goodstein's theorem; Green's theorem (to do) Green's theorem when D is a simple region; Heine–Borel theorem; Intermediate value theorem; Itô's lemma; Kőnig's lemma; Kőnig's theorem (set theory) Kőnig's theorem (graph theory) Lagrange's theorem (group theory) Lagrange's theorem (number theory)
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.
Graph pebbling is a mathematical game played on a graph with zero or more pebbles on each of its vertices. 'Game play' is composed of a series of pebbling moves. A pebbling move on a graph consists of choosing a vertex with at least two pebbles, removing two pebbles from it, and adding one to an adjacent vertex (the second removed pebble is discarded from play). π(G), the pebbling number of a ...