3-Graph Coloring: Difference between revisions
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== Parameters == | == Parameters == | ||
n: number of vertices | $n$: number of vertices | ||
m: number of edges | $m$: number of edges | ||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 24: | Line 24: | ||
|- | |- | ||
| [[Brute-force search (3-Graph Coloring Graph Coloring)|Brute-force search]] || 1852 || $O((n | | [[Brute-force search (3-Graph Coloring Graph Coloring)|Brute-force search]] || 1852 || $O((m+n)*{3}^n)$ || $O(n)$ auxiliary || Exact || Deterministic || | ||
|- | |- | ||
| [[ | | [[Brélaz (DSatur) (3-Graph Coloring Graph Coloring)|Brélaz (DSatur)]] || 1979 || $O(n^{2})$ || $O(m+n)$ || Exact || Deterministic || [https://dl.acm.org/doi/10.1145/359094.359101 Time] | ||
|- | |- | ||
| [[ | | [[Petford and Welsh (3-Graph Coloring Graph Coloring)|Petford and Welsh]] || 1989 || $O(n \log n)$ || $O(n)$ || Exact || Randomized || [https://www.sciencedirect.com/science/article/pii/0012365X89902148 Time] | ||
|- | |- | ||
| [[Lawler (3-Graph Coloring Graph Coloring)|Lawler]] || 1976 || $O(m*n*{3}^{(n/{3})}) ~ O(mn({1.445})^n)$ || $O(n)$ || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/002001907690065X?via%3Dihub Time] | |||
| [[Lawler (3-Graph Coloring Graph Coloring)|Lawler]] || 1976 || $O(m*n*{3}^{(n/{3})}) ~ O(mn({1.445})^n)$ || $O(n | |||
|- | |- | ||
| [[Schiermeyer (3-Graph Coloring Graph Coloring)|Schiermeyer]] || 1994 || $O({1.415}^n)$ || $O(nm+n^{2})$ loose bound, possibly $O(n+m)$? || Exact || Deterministic || [https://link.springer.com/chapter/10.1007/3-540-57899-4_51 Time] | | [[Schiermeyer (3-Graph Coloring Graph Coloring)|Schiermeyer]] || 1994 || $O({1.415}^n)$ || $O(nm+n^{2})$ loose bound, possibly $O(n+m)$? || Exact || Deterministic || [https://link.springer.com/chapter/10.1007/3-540-57899-4_51 Time] | ||
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|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:Graph Coloring - 3-Graph Coloring - Time.png|1000px]] | [[File:Graph Coloring - 3-Graph Coloring - Time.png|1000px]] | ||
== References/Citation == | == References/Citation == | ||
https://www.sciencedirect.com/science/article/pii/S0196677404001117?via%3Dihub | https://www.sciencedirect.com/science/article/pii/S0196677404001117?via%3Dihub | ||
Latest revision as of 09:12, 28 April 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 | $O((m+n)*{3}^n)$ | $O(n)$ auxiliary | Exact | Deterministic | |
| Brélaz (DSatur) | 1979 | $O(n^{2})$ | $O(m+n)$ | Exact | Deterministic | Time |
| Petford and Welsh | 1989 | $O(n \log n)$ | $O(n)$ | Exact | Randomized | Time |
| Lawler | 1976 | $O(m*n*{3}^{(n/{3})}) ~ O(mn({1.445})^n)$ | $O(n)$ | 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
References/Citation
https://www.sciencedirect.com/science/article/pii/S0196677404001117?via%3Dihub