4-Graph Coloring (Graph Coloring)

From Algorithm Wiki
Jump to navigation Jump to search


In this case, we wish to determine whether or not a graph is 4-colorable.

Related Problems

Generalizations: k-Graph Coloring

Related: Chromatic Number, 2-Graph Coloring, 3-Graph Coloring, 5-Graph Coloring, #k-Graph Coloring, #2-Graph Coloring, #3-Graph Coloring, #4-Graph Coloring, #5-Graph Coloring


$n$: number of vertices

$m$: number of edges

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Brute force 1852 $O((m+n)*{4}^n)$ $O(n)$ auxiliary Exact Deterministic
Fomin; Gaspers & Saurabh 2007 $O({1.7272}^n)$ $O(n)$ Exact Deterministic Time
Lawler 1976 $O((m + n)*{2}^n)$ $O(n)$ Exact Deterministic Time
Byskov 2004 $O({1.7504}^n)$ $O(n^{2})$? Exact Deterministic Time

Time Complexity Graph

Graph Coloring - 4-Graph Coloring - Time.png