Search results
Results From The WOW.Com Content Network
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study the four color problem .
To compute the chromatic number and the chromatic polynomial, this procedure is used for every =, …,, impractical for all but the smallest input graphs. Using dynamic programming and a bound on the number of maximal independent sets , k -colorability can be decided in time and space O ( 2.4423 n ) {\displaystyle O(2.4423^{n})} . [ 13 ]
The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f ( v ) to each vertex v , a graph G is f -choosable (or f -list-colorable ) if it has a list coloring no matter how one assigns a list of f ( v ...
The chromatic symmetric function is a symmetric function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight generating function for proper graph colorings , and was originally introduced by Richard Stanley as a generalization of the chromatic polynomial of a graph.
Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial
If such a k-coloring exists, then we refer to the smallest k needed in order to properly color our graph as the chromatic number, denoted by χ(G). [2] The number of proper k -colorings is a polynomial function of k called the chromatic polynomial of our graph G (by analogy with the chromatic polynomial of undirected graphs) and can be denoted ...
The equitable chromatic number of a graph G is the smallest number k such that G has an equitable coloring with k colors. But G might not have equitable colorings for some larger numbers of colors; the equitable chromatic threshold of G is the smallest k such that G has equitable colorings for any number of colors greater than or equal to k .
Characteristic polynomial of a graph; Cheeger constant (graph theory) Chromatic number; Chromatic polynomial; Circuit rank; Circular chromatic number; Circumference (graph theory) Clique number; Clique-width; Closeness centrality; Clustering coefficient; Colin de Verdière graph invariant; Conductance (graph theory) Connected domination number ...