6-coloring Algorithm

eldamutia

22 Feb, 2022

Stant factor algorithm for 6-coloring planar graphs and with less colors for related families. More speci cally we obtain a deterministic Ologn time.

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Kempes graph-coloring algorithm To 6-color a planar graph.

6-coloring algorithm. The root assigns itself the label 0 3. Algorithm 4 6-Color 1. Send own color c v to all children 5.

Color the rest of the graph with a recursive call to Kempes algorithm. Each other node v executes the following code 4. ALGORITHM 6 COLOR.

Assume that initially the nodes have IDs of size logn bits 2. Every planar graph has at least one vertex of degree 5. Given an n vertex planar graph G in adjacency list form this algorithm determines a 6-coloring of G.

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