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Graph minor Wagner's theorem: Outerplanar graphs: K 4 and K 2,3: Graph minor Diestel (2000), [1] p. 107: Outer 1-planar graphs: Six forbidden minors Graph minor Auer et al. (2013) [2] Graphs of fixed genus: A finite obstruction set Graph minor Diestel (2000), [1] p. 275: Apex graphs: A finite obstruction set Graph minor [3] Linklessly ...
Switching {X,Y} in a graph. A two-graph is equivalent to a switching class of graphs and also to a (signed) switching class of signed complete graphs.. Switching a set of vertices in a (simple) graph means reversing the adjacencies of each pair of vertices, one in the set and the other not in the set: thus the edge set is changed so that an adjacent pair becomes nonadjacent and a nonadjacent ...
Former logo of Dialog. Orange România is a broadband Internet service provider and mobile provider in Romania. It is Romania's largest GSM network operator [3] which is majority owned by Orange S.A. that also uses some of the Telekom Romania infrastructure, the biggest initial investor, who gradually increased its ownership.
For arbitrary graph families, and arbitrary sentences, this problem is undecidable. However, satisfiability of MSO 2 sentences is decidable for the graphs of bounded treewidth, and satisfiability of MSO 1 sentences is decidable for graphs of bounded clique-width. The proof involves using Courcelle's theorem to build an automaton that can test ...
Every bipartite graph G = (X+Y, E) is 2-colorable: each edge contains exactly one vertex of X and one vertex of Y, so e.g. X can be colored blue and Y can be colored yellow and no edge is monochromatic. The property of 2-colorability was first introduced by Felix Bernstein in the context of set families; [1] therefore it is also called Property B.
If H is a two-vertex complete graph K 2, then for any graph G, the rooted product of G and H has domination number exactly half of its number of vertices. Every connected graph in which the domination number is half the number of vertices arises in this way, with the exception of the four-vertex cycle graph .
The Grötzsch graph is a triangle-free graph that cannot be colored with fewer than four colors. Much research about triangle-free graphs has focused on graph coloring. Every bipartite graph (that is, every 2-colorable graph) is triangle-free, and Grötzsch's theorem states that every triangle-free planar graph may be 3-colored. [8]
In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color. When k = 2 these are the bipartite graphs, and when k = 3 they are called the ...