### Graph Vertices Coloring

- Assign a color to each vertex of the graph such that no two adjacent vertices have same color
- Minimum number of color used for proper coloring of a graph is known chromatic number of the graph
- The chromatic number of graph G denoted χ(G), is the smallest k such that G is K-colorable

Facts

- If a G has n vertices, χ(G) <= n
- χ(G)= 1, iff G has on edges
- χ (even-cycle) = 2 and χ(odd-cycle) = 3
- χ(complete G) = n
- if H is a subgraph of then χ(G) >= χ(H)
- For G(V,E) – A K-coloring of G partitions the vertex set V into K sets v1, v2 ……. Vk where each vi is an independent set

**Application**

- Scheduling is one of its application

Solution:

- For small problem, backtracking approach works, however the graph coloring problem is known as
- NP hard problem.
- Backtracking takk O(m^n) where m => number of color and n=> number of vertices

##### Algorithm:

- Iterate all color one by one
- Check is it safe to assign current color for vertex v
- If yes then
- assign color to vertex v
- Recursively call for next vertex

Latest Source Code:

Github: GraphColoring.java

**Output:**

Vertex Color 0 RED 1 GREEN 2 RED 3 YELLOW