Graph Coloring Solver

Overview

The Graph Coloring Solver demonstrates algorithms for assigning colors to graph vertices such that no two adjacent vertices share the same color. Watch as greedy and backtracking algorithms attempt to color the graph with the minimum number of colors. The chromatic number (minimum colors needed) is a fundamental graph property. Perfect for understanding register allocation, scheduling, map coloring, and constraint satisfaction problems.

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Tips

  • The chromatic number is the minimum colors needed to color the graph properly
  • Greedy coloring is fast but may not use the minimum number of colors
  • Backtracking can find optimal coloring but is slower for large graphs
  • Vertex ordering affects greedy coloring results - try different orderings
  • Applications: register allocation in compilers, scheduling, frequency assignment
  • Some graphs have special chromatic numbers: bipartite graphs need 2, complete graphs need n
  • Watch how the algorithm assigns colors and backtracks when it gets stuck
  • Try well-known graphs like complete, bipartite, and cycle graphs