Perfect colorings of $Z^2$: Nine colors
Denis Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)
TL;DR
This paper comprehensively enumerates all perfect colorings of the two-dimensional integer lattice using up to nine colors, providing a complete classification for this combinatorial problem.
Contribution
It offers the first complete listing of perfect colorings of Z^2 with nine or fewer colors, advancing understanding of equitable partitions in lattice graphs.
Findings
All perfect colorings of Z^2 with ≤9 colors are listed.
Provides a classification framework for equitable partitions.
Completes the enumeration for nine-color perfect colorings.
Abstract
We list all perfect colorings of by 9 or less colors. Keywords: perfect colorings, equitable partitions
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Taxonomy
TopicsAdvanced Mathematical Theories · Graph Labeling and Dimension Problems · Color Science and Applications