Search results
Results From The WOW.Com Content Network
In graph theory, a path in an edge-colored graph is said to be rainbow if no color repeats on it. A graph is said to be rainbow-connected (or rainbow colored ) if there is a rainbow path between each pair of its vertices .
In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling.
A proper edge-coloring does not guarantee the existence of a perfect rainbow matching. For example, consider the graph K 2,2: the complete bipartite graph on 2+2 vertices. Suppose the edges (x 1,y 1) and (x 2,y 2) are colored green, and the edges (x 1,y 2) and (x 2,y 1) are colored blue. This is a proper coloring, but there are only two perfect ...
Graph theory in sociology: Moreno Sociogram (1953). [16] Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [17]
In graph theory, path coloring usually refers to one of two problems: The problem of coloring a (multi)set of paths R {\displaystyle R} in graph G {\displaystyle G} , in such a way that any two paths of R {\displaystyle R} which share an edge in G {\displaystyle G} receive different colors.
In graph theory, a rainbow-independent set (ISR) is an independent set in a graph, in which each vertex has a different color. Formally, let G = (V, E) be a graph, and suppose vertex set V is partitioned into m subsets V 1, …, V m, called "colors". A set U of vertices is called a rainbow-independent set if it satisfies both the following ...
In graph theory, an area of mathematics, an equitable coloring is an assignment of colors to the vertices of an undirected graph, in such a way that No two adjacent vertices have the same color, and; The numbers of vertices in any two color classes differ by at most one.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.