Distance Coloring of the Hexagonal Lattice
Copyright policy )Distance Coloring of the Hexagonal Lattice
The authors show that the \(d\)-distant chromatic number \(\chi_d(H)\) of the hexagonal lattice \(H\) is (i) \(\chi_d(H)=[\frac 38(d+1)^2]\) for every odd \(d\geq 1\), (ii) \(\frac 38 d^2+\frac 34 d+2\leq\chi_d(H)\leq[\frac 38 (d+\frac 43)^2]\) for every even \(d\geq 8\), where \(\chi_2(H)=4\), \(\chi_4(H)=11\), \(\chi_6(H)=20\). The following conjecture is stated: For every even \(d\geq 2\) we have \(\chi_d(H)=[\frac 38(d+\frac 43)^2]\).
- Carlos III University of Madrid Spain
- Lancaster University United Kingdom
Coloring of graphs and hypergraphs, Distance in graphs, hexagonal grid, radio channel frequency assignment, distant chromatic number, hexagonal tiling, 510, 004
Coloring of graphs and hypergraphs, Distance in graphs, hexagonal grid, radio channel frequency assignment, distant chromatic number, hexagonal tiling, 510, 004
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