Graph Coloring Challenge

3

Color all vertices so that no two adjacent vertices have the same color!

Available Colors:

Click a color, then click a vertex to color it.

Graph Parameters

Parameters

Graph Info

Vertices: 6

Edges: 0

Chromatic Number: -

How to Use This Experiment

Instructions

• Select a color from the palette below the challenge.

• Click a vertex on the graph to color it with the selected color.

• Use "Check Coloring" to verify your solution.

• Click "Show Solution" to see an automatic coloring.

• "New Graph" generates a different random graph.

• "Clear Colors" removes all your coloring.

Adjust Parameters

• Click the floating controls button (bottom right) to open the parameters panel.

• Change the number of vertices or colors using the sliders.

• The graph and challenge will update automatically.

Tips

• No two connected vertices can have the same color.

• Try to use as few colors as possible.

• Use the info and controls panels for help and customization.

Vertex Coloring

Vertex coloring assigns colors to vertices such that no two adjacent vertices share the same color.

Chromatic Number χ(G):

The minimum number of colors needed to properly color a graph.

Examples:

  • Bipartite graphs: χ(G) = 2
  • Complete graph K_n: χ(G) = n
  • Trees: χ(G) = 2

Algorithms & Applications

Graph coloring has numerous real-world applications and algorithmic approaches.

Greedy Algorithm:

Color vertices in order, using the smallest available color for each vertex.

Applications:

  • Course scheduling
  • Register allocation
  • Map coloring
  • Frequency assignment