Distance coloring of the hexagonal lattice

• Autorzy: Peter Jacko , Stanislav Jendrol'
• Języki publikacji: EN

Abstrakty

EN

Motivated by the frequency assignment problem we study the d-distant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted $χ_d(H)$, is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of $χ_d(H)$ for any d odd and estimations for any d even.

Słowa kluczowe

EN

distance coloring; distant chromatic number; hexagonal lattice of the plane; hexagonal tiling; hexagonal grid; radio channel frequency assignment

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C15: Coloring of graphs and hypergraphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 151-166

Daty

wydano

2005

otrzymano

2003-11-25

poprawiono

2005-02-22

Twórcy

autor

Peter Jacko

• Universidad Carlos III de Madrid, Department of Business Administration, Calle Madrid 126, 289 03 Getafe (Madrid), Spain

autor

Stanislav Jendrol'

• P.J. Šafárik University, Institute of Mathematics, Jesenná 5, 041 54 Košice, Slovakia

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1269