DSA
    intermediate

    Graph Coloring (Greedy)

    Graph Coloring (Greedy)

    Assign colors to vertices such that no two adjacent vertices share the same color. The greedy approach gives an upper bound on the chromatic number.

    ⏱ O(V+E)
    💾 O(V)
    Ready
    Red
    Green
    Blue
    Orange

    Starting Greedy Graph Coloring

    50%
    Live Variables
    nodes6
    edges9

    Greedy colouring

    Sequence

    Order the steps of the greedy colouring algorithm.

    Tap a piece, then tap where it goes — or drag it. Tap the tray to take one back.

    1. 1Drop a step here
    2. 2Drop a step here
    3. 3Drop a step here
    4. 4Drop a step here
    5. 5Drop a step here
    5 pieces left to place

    Test your knowledge

    20 questions
    Question 1 of 20
    Score: 0

    What is the chromatic number of a graph?

    The short version

    Think of scheduling exams. No two exams can happen simultaneously if they share students. Assigning time slots is like coloring: adjacent nodes (shared students) need different colors (times).

    In more depth

    Greedy Coloring Algorithm

    1.Order vertices (any order works)
    2.For each vertex:
    Look at neighbors' colors
    Assign smallest color not used by neighbors

    Properties

    Greedy may not give optimal (minimum) colors
    Optimal graph coloring is NP-Complete
    Order of vertices affects result

    Applications

    Exam scheduling
    Register allocation in compilers
    Map coloring
    Frequency assignment in wireless networks

    When to reach for this

    • Assign labels with adjacency constraints
    • Scheduling with conflicts
    • Partitioning into independent sets
    • Keywords: 'no two adjacent', 'bipartite', 'conflict'

    Interview Questions

    Meta
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    Amazon
    Airbnb
    Uber
    Meta
    Microsoft
    Bloomberg
    Palantir
    Netflix
    LinkedIn

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