Perfect 2‐colorings of Hamming graphs
Copyright policy )Perfect 2‐colorings of Hamming graphs
AbstractWe consider the problem of existence of perfect 2‐colorings (equitable 2‐partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe known constructions of perfect colorings and propose some new ones giving new parameters. At last, we deduce which parameters of colorings are covered by these constructions and give tables of admissible parameters of 2‐colorings in Hamming graphs for small and . Using the connection with perfect colorings, we construct an orthogonal array OA(2048, 7, 4, 5).
- Novosibirsk State University Russian Federation
- Sobolev Institute of Mathematics Russian Federation
Coloring of graphs and hypergraphs, Hamming graph, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), graph covering, FOS: Mathematics, perfect code, Mathematics - Combinatorics, perfect coloring, Orthogonal arrays, Latin squares, Room squares, equitable partition, Combinatorics (math.CO)
Coloring of graphs and hypergraphs, Hamming graph, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), graph covering, FOS: Mathematics, perfect code, Mathematics - Combinatorics, perfect coloring, Orthogonal arrays, Latin squares, Room squares, equitable partition, Combinatorics (math.CO)
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