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In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
In graph theory, a cycle in a graph is a non-empty trail in which only the first and last vertices are equal. A directed cycle in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.
22 wrz 2024 · A graph is a circle graph if it is the intersection graph of chords in a circle. Let the local complement G*v result from G by complementing G[N(v)]. Two graphs are said to be locally equivalent if one results from the other by a series of local complements.
Graph theory is the study of mathematical objects known as graphs, which consist of vertices (or nodes) connected by edges. (In the figure below, the vertices are the numbered circles, and the edges join the vertices.)
11 wrz 2019 · Berkeley Math Circle: Graph Theory Olympiad Graph Theory Problems: • (IMO 2001 Shortlist) Define a k-clique to be a set of k people such that every pair of them are acquainted with each other. At a certain party, every pair of 3-cliques has at least one person in common, and there are no 5-cliques.
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).
A graph is called a circle graph if each of its vertices can be associated with a chord on a circle in such a way that two vertices are adjacent if and only if their associated chords cross inside the circle.
