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Graph Coloring Applications

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Graph Coloring Applications

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Now · Scheduling

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


python
def 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

\Delta + 1

colors (where

\Delta

is max degree). Join Discord PreviousGraph Coloring & PlanarityNextEulerian & Hamiltonian

Graph Coloring Applications

Graph Coloring Applications

Scheduling

Map Coloring

Greedy Coloring Algorithm

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