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The complement graph of a complete graph is an empty graph. If the edges of a complete graph are each given an orientation, the resulting directed graph is called a tournament. K n can be decomposed into n trees T i such that T i has i vertices. [6] Ringel's conjecture asks if the complete graph K 2n+1 can be decomposed into copies of any tree ...
Complete directed graphs are simple directed graphs where each pair of vertices is joined by a symmetric pair of directed arcs (it is equivalent to an undirected complete graph with the edges replaced by pairs of inverse arcs). It follows that a complete digraph is symmetric.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
A directed graph or digraph is a graph in which edges have orientations. ... or decomposing a complete graph K n into n − 1 specified trees having, respectively, 1 ...
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions. Equivalently, a tournament is an orientation of an undirected complete graph.
As complete graphs are Hamiltonian, all graphs whose closure is complete are Hamiltonian, which is the content of the following earlier theorems by Dirac and Ore. Dirac's Theorem (1952) — A simple graph with n vertices ( n ≥ 3 {\displaystyle n\geq 3} ) is Hamiltonian if every vertex has degree n 2 {\displaystyle {\tfrac {n}{2}}} or greater.
A tournament is an orientation of a complete graph; that is, it is a directed graph such that every two vertices are connected by exactly one directed edge (going in only one of the two directions between the two vertices). traceable A traceable graph is a graph that contains a Hamiltonian path. trail A walk without repeated edges. transitive
This is the directed-graph analogue of what (above) has been called R(n, n; 2), the smallest number Z such that any 2-colouring of the edges of a complete undirected graph with ≥ Z nodes, contains a monochromatic complete graph on n nodes. (The directed analogue of the two possible arc colours is the two directions of the arcs, the analogue ...