3-Graph Coloring: Difference between revisions
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== | == Time-Space Tradeoff == | ||
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Revision as of 14:48, 15 February 2023
Description
In this case, we wish to determine whether or not a graph is 3-colorable.
Related Problems
Generalizations: k-Graph Coloring
Related: Chromatic Number, 2-Graph Coloring, 4-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring
Parameters
n: number of vertices
m: number of edges
Table of Algorithms
Name | Year | Time | Space | Approximation Factor | Model | Reference |
---|---|---|---|---|---|---|
Brute-force search | 1852 | $O((n+m)*{3}^n)$ | $O(n)$ auxiliary | Exact | Deterministic | |
Karger, Blum | 1997 | $O(poly(V))$ | $\tilde{O}(n^{3/14})$ | Deterministic | Time | |
Brélaz (DSatur) | 1979 | $O(V^{2})$ | $O(V + E)$ | Exact | Deterministic | Time |
Petford and Welsh | 1989 | $O(nlogn)$ | $O(n)$ | Exact | Randomized | Time |
Lawler | 1976 | $O(m*n*{3}^{(n/{3})}) ~ O(mn({1.445})^n)$ | $O(n+m)$ | Exact | Deterministic | Time |
Schiermeyer | 1994 | $O({1.415}^n)$ | $O(nm+n^{2})$ loose bound, possibly $O(n+m)$? | Exact | Deterministic | Time |
Beigel & Eppstein | 1995 | $O({1.3446}^n)$ | $O(n^{2})$? | Exact | Deterministic | Time |
Beigel & Eppstein | 2000 | $O({1.3289}^n)$ | $O(n^{2})$? | Exact | Deterministic | Time |
Robson | 1986 | $O({1.2108}^n)$ | Exact | Deterministic | Time | |
Schöning | 1999 | $O({1.333}^n)$ | Exact | Randomized | Time | |
Hirsch | 1998 | $O({1.239}^n)$ | Exact | Deterministic | Time | |
Johnson | 1988 | $O({1.4422}^n)$ | Exact | Deterministic | Time | |
Alon and Kahale | 1997 | $O({1.24}^n)$ | Exact | Deterministic | Time |
Time Complexity Graph
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Space Complexity Graph
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Time-Space Tradeoff
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