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Total coloring via efficient dominating sets

Published on:

14 May 2024

Primary Category:

Combinatorics

Paper Authors:

Italo J. Dejter

Bullets

Key Details

Proves 3-cube graph has totally efficient 4-coloring with vertex color classes as efficient dominating sets

Conjectures 3-cube is only such case of totally effective coloring

Relates to edge-girth colorings of prism graphs of star transposition graphs

Shows totally efficient colorings can yield orthogonal 1-factorizations

Extends 3-cube efficient coloring to produce edge-girth 4-cube coloring

AI generated summary

Total coloring via efficient dominating sets

This paper studies total colorings of graphs where each vertex color class forms an efficient dominating set, meaning a minimal set that is within 1 edge of every vertex. It proves the 3-cube graph has such a coloring using 4 colors, and conjectures this is the only such case. It relates this to edge colorings of prism graphs formed from star transposition graphs.

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