4 - Graph Coloring: Difference between revisions
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== Problem Description== | |||
Graph coloring problem is to assign colors to certain elements of a graph subject to certain constraints. | |||
Vertex coloring is the most common graph coloring problem. The problem is, given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color. The other graph coloring problems like Edge Coloring (No vertex is incident to two edges of same color) and Face Coloring (Geographical Map Coloring) can be transformed into vertex coloring. | |||
== Bounds Chart == | |||
[[File:4_-_Graph_ColoringBoundsChart.png|1050px]] | |||
== Step Chart == | |||
[[File:4_-_Graph_ColoringStepChart.png|1050px]] | |||
== Improvement Table == | |||
{| class="wikitable" style="text-align:center;" width="100%" | |||
!width="20%" | Complexity Classes !! width="40%" | Algorithm Paper Links !! width="40%" | Lower Bounds Paper Links | |||
|- | |||
| rowspan="1" | Exp/Factorial | |||
| [ Brute force (1852)] | |||
[https://www.sciencedirect.com/science/article/pii/002001907690065X?via%3Dihub Lawler; 1976 (1976)] | |||
[https://www.sciencedirect.com/science/article/abs/pii/S0167637704000409?via%3Dihub Byskob 2004 (2004)] | |||
[https://link.springer.com/chapter/10.1007/978-3-540-73545-8_9 Fomin; Gaspers & Saurabh (2007) (2007)] | |||
| | |||
|- | |||
| rowspan="1" | Polynomial > 3 | |||
| | |||
| | |||
|- | |||
| rowspan="1" | Cubic | |||
| | |||
| | |||
|- | |||
| rowspan="1" | Quadratic | |||
| | |||
| | |||
|- | |||
| rowspan="1" | nlogn | |||
| | |||
| | |||
|- | |||
| rowspan="1" | Linear | |||
| | |||
| | |||
|- | |||
| rowspan="1" | logn | |||
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|-|} | |||
Latest revision as of 11:53, 10 October 2022
Problem Description
Graph coloring problem is to assign colors to certain elements of a graph subject to certain constraints.
Vertex coloring is the most common graph coloring problem. The problem is, given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color. The other graph coloring problems like Edge Coloring (No vertex is incident to two edges of same color) and Face Coloring (Geographical Map Coloring) can be transformed into vertex coloring.
Bounds Chart
Step Chart
Improvement Table
| Complexity Classes | Algorithm Paper Links | Lower Bounds Paper Links |
|---|---|---|
| Exp/Factorial | [ Brute force (1852)] | |
| Polynomial > 3 | ||
| Cubic | ||
| Quadratic | ||
| nlogn | ||
| Linear | ||
| logn |