Graph Coloring Applications
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Python
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Python Week 1: the first filter for runtime behavior
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# Graph Coloring Applications ## Scheduling **Problem:** Schedule exams so no student has two at the same time. **Model:** Vertices = exams, edge if shared student.
Graph Coloring Applications
Scheduling
Problem: Schedule exams so no student has two at the same time. Model: Vertices = exams, edge if shared student. Chromatic number = minimum time slots.
Map Coloring
Four Color Theorem: Every planar graph is 4-colorable (Appel & Haken, 1976).
Proof: First major theorem proved by computer. 1936 configurations checked by program.
Greedy Coloring Algorithm
pythondef greedy_coloring(graph): colors = {} for v in sorted(graph, key=lambda x: len(graph[x]), reverse=True): used = {colors[n] for n in graph[v] if n in colors} color = 0 while color in used: color += 1 colors[v] = color return colors
The greedy algorithm uses at most colors (where is max degree).
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