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Chromatic Polynomial: Difference between revisions
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(Created page with "== Introduction == The chromatic polynomial is a graph-theoretic function that provides important information about the colorability of a graph. It was first introduced by George David Birkhoff in his attempt to solve the four-color problem. The chromatic polynomial counts the number of ways a graph can be colored using at most k colors, such that no two adjacent vertices share the same color. The chromatic polynomial is a fundamental object in algebraic graph theory, a...") |
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Computing the chromatic polynomial of a graph is a challenging problem. The most straightforward method is to use the deletion-contraction algorithm, which is based on the recursive formula: P(G, k) = P(G-e, k) - P(G/e, k), where G-e is the graph obtained by deleting an edge e from G, and G/e is the graph obtained by contracting e in G. However, this algorithm has exponential time complexity, making it impractical for large graphs. | Computing the chromatic polynomial of a graph is a challenging problem. The most straightforward method is to use the deletion-contraction algorithm, which is based on the recursive formula: P(G, k) = P(G-e, k) - P(G/e, k), where G-e is the graph obtained by deleting an edge e from G, and G/e is the graph obtained by contracting e in G. However, this algorithm has exponential time complexity, making it impractical for large graphs. | ||
[[Image:Detail-147043.jpg|thumb|center|A graph with vertices and edges, suitable for illustrating the concept of chromatic polynomial.]] | |||
== Applications == | == Applications == | ||