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Calcimator

Chromatic Number Estimator

Estimate the chromatic number of a graph using Brook's theorem and greedy coloring bounds.

Inputs

Results

Greedy Coloring Estimate

4

Brook's Bound

4

Upper Bound (Δ+1)5
How to Use This Calculator
  1. Enter the number of Vertices and Edges in your graph.
  2. Input the Maximum Degree of any vertex.
  3. Review the Upper Bound (Max Degree + 1) from Vizing's theorem and the Brooks Bound for non-complete, non-odd-cycle graphs.
  4. Check the Greedy Coloring Estimate — this is a practical upper bound for sparse graphs.
  5. Use these bounds to determine the minimum colors needed before running an exact coloring algorithm.
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