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.
- The chromatic number is an essential parameter that captures the inherent colorability of a graph.
- It provides insights into the structural properties and relationships within the graph.
Vertex Coloring:
- A vertex coloring of a graph assigns colors to its vertices in a way that no two adjacent vertices have the same color.
- Proper vertex coloring ensures that adjacent vertices have distinct colors.
Chromatic Number of a Graph | Graph Colouring
Graph coloring is a fundamental concept in graph theory, and the chromatic number is a key parameter that quantifies the coloring properties of a graph. Let’s go into the introductory aspects of the chromatic number.
Graph coloring refers to the problem of coloring vertices of a graph in such a way that no two adjacent vertices have the same color. This is also called the vertex coloring problem. If coloring is done using at most m colors, it is called m-coloring.
Table of Content
- What is Chromatic Number?
- Chromatic Number of Cyclic Graph:
- Chromatic Number of Complete Graph:
- Chromatic Number of Bipartite Graph:
- Chromatic Number of Star Graph:
- Chromatic Number of Wheel Graph:
- Chromatic Number of Planar Graph:
- Properites of Chromatic Number:
- Importance of Chromatic Number in Graph Theory:
- Algorithm to Find Chromatic Numbers
- Choosing the right algorithm for finding chromatic number depends on the specific graph:
- Relation between chromatic number and chromatic polynomial
- Analogy:
- Related Articles:
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