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Distance coloring of the hexagonal lattice

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Distance coloring of the hexagonal lattice. / Jacko, Peter; Jendrol', Stanislav.
In: Discussiones Mathematicae Graph Theory, Vol. 25, No. 1-2, 2005, p. 151-166.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Jacko, P & Jendrol', S 2005, 'Distance coloring of the hexagonal lattice', Discussiones Mathematicae Graph Theory, vol. 25, no. 1-2, pp. 151-166. https://doi.org/10.7151/dmgt.1269

APA

Jacko, P., & Jendrol', S. (2005). Distance coloring of the hexagonal lattice. Discussiones Mathematicae Graph Theory, 25(1-2), 151-166. https://doi.org/10.7151/dmgt.1269

Vancouver

Jacko P, Jendrol' S. Distance coloring of the hexagonal lattice. Discussiones Mathematicae Graph Theory. 2005;25(1-2):151-166. doi: 10.7151/dmgt.1269

Author

Jacko, Peter ; Jendrol', Stanislav. / Distance coloring of the hexagonal lattice. In: Discussiones Mathematicae Graph Theory. 2005 ; Vol. 25, No. 1-2. pp. 151-166.

Bibtex

@article{8230c98649e94721bb63b01a593429f4,
title = "Distance coloring of the hexagonal lattice",
abstract = "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 χd(H), is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of χd(H) for any d odd and estimations for any d even.",
keywords = "distance coloring, distant chromatic number , hexagonal lattice of the plane , hexagonal tiling , hexagonal grid , radio channel frequency assignment",
author = "Peter Jacko and Stanislav Jendrol'",
year = "2005",
doi = "10.7151/dmgt.1269",
language = "English",
volume = "25",
pages = "151--166",
journal = "Discussiones Mathematicae Graph Theory",
issn = "1234-3099",
publisher = "University of Zielona Gora",
number = "1-2",

}

RIS

TY - JOUR

T1 - Distance coloring of the hexagonal lattice

AU - Jacko, Peter

AU - Jendrol', Stanislav

PY - 2005

Y1 - 2005

N2 - 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 χd(H), is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of χd(H) for any d odd and estimations for any d even.

AB - 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 χd(H), is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of χd(H) for any d odd and estimations for any d even.

KW - distance coloring

KW - distant chromatic number

KW - hexagonal lattice of the plane

KW - hexagonal tiling

KW - hexagonal grid

KW - radio channel frequency assignment

U2 - 10.7151/dmgt.1269

DO - 10.7151/dmgt.1269

M3 - Journal article

VL - 25

SP - 151

EP - 166

JO - Discussiones Mathematicae Graph Theory

JF - Discussiones Mathematicae Graph Theory

SN - 1234-3099

IS - 1-2

ER -