Chromatic Number of a Graph | Graph Colouring - GeeksforGeeks
2024年7月9日 · What is Chromatic Number? The chromatic number of a graph G, denoted as χ (G), is the minimum number of colors required to color the vertices of a graph G in such a way that no two adjacent vertices share the same color. Formally, it is the smallest positive integer k for which there exists a proper vertex coloring with k colors.
Graph coloring - Wikipedia
For chordal graphs, and for special cases of chordal graphs such as interval graphs and indifference graphs, the greedy coloring algorithm can be used to find optimal colorings in polynomial time, by choosing the vertex ordering to be the reverse of a perfect elimination ordering for the graph.
Chromatic Number -- from Wolfram MathWorld
2 天之前 · Computation of the chromatic number of a graph is implemented in the Wolfram Language as VertexChromaticNumber [g]. Precomputed chromatic numbers for many named graphs can be obtained using GraphData [graph, "ChromaticNumber"]. The chromatic number of a graph must be greater than or equal to its clique number.
Chromatic Number of graphs | Graph coloring in Graph theory
In other words, the chromatic number can be described as a minimum number of colors that are needed to color any graph in such a way that no two adjacent vertices of a graph will be assigned the same color.
Graph Coloring and Chromatic Numbers - Brilliant
The chromatic number \(\chi(G)\) of a graph \(G\) is the minimal number of colors for which such an assignment is possible. Other types of colorings on graphs also exist, most notably edge colorings that may be subject to various constraints.
Chromatic Number - D3 Graph Theory
Chromatic number of a graph is the minimum value of k k for which the graph is k-c o l o r a b l e k-c o l o r a b l e. In other words, it is the minimum number of colors needed for a proper-coloring of the graph.
De nition 16 (Chromatic Number). The chromatic number of a graph is the minimum number of colors in a proper coloring of that graph. How do we determine the chromatic number of a graph? In the last example, we did it by rst nding a 4-coloring, and then making an intricate argument that a 3-coloring would be impossible.
5.8: Graph Coloring - Mathematics LibreTexts
Definition \(\PageIndex{3}\): Chromatic Number. The chromatic number of a graph \(G\) is the minimum number of colors required in a proper coloring; it is denoted \(\chi(G)\).
Optimization Problems Given a graph G, what is the least t so that G has a t-coloring? This integer is called the chromatic number of G and is denoted χ(G). The coloring below is the same graph but now we illustrate a 5-coloring, so χ(G) ≤ 5.
Chromatic Polynomials. In this subsection we introduce an important tool to study graph coloring, the chromatic polynomial. Proposition 6. Let Gbe a simple graph with labeled vertices. For every k2N, let p k denote the number of proper k-coloring of G. Then there exists a unique polynomial p(x) 2Q[x] such that p(k) = p k for every k2N. Proof ...