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## Discussiones Mathematicae Graph Theory

2005 | 25 | 1-2 | 151-166
Tytuł artykułu

### Distance coloring of the hexagonal lattice

Autorzy
Treść / Zawartość
Warianty tytułu
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
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
151-166
Opis fizyczny
Daty
wydano
2005
otrzymano
2003-11-25
poprawiono
2005-02-22
Twórcy
autor
autor
• P.J. Šafárik University, Institute of Mathematics, Jesenná 5, 041 54 Košice, Slovakia
Bibliografia
• [1] G.J. Chang and D. Kuo, The L(2,1)-labeling problem on graphs, SIAM J. Discrete Math. 9 (1996) 309-316, doi: 10.1137/S0895480193245339.
• [2] G. Fertin, E. Godard and A. Raspaud, Acyclic and k-distance coloring of the grid, Information Processing Letters 87 (2003) 51-58, doi: 10.1016/S0020-0190(03)00232-1.
• [3] J.P. Georges and D.M. Mauro, Generalized vertex labelings with a condition at distance two, Congr. Numer. 109 (1995) 141-159.
• [4] J.R. Griggs and R.K. Yeh, Labelling graphs with a condition at distance 2, SIAM J. Discrete Math. 5 (1992) 586-595, doi: 10.1137/0405048.
• [5] W.K. Hale, Frequency assignment: theory and applications, Proc. IEEE 68 (1980) 1497-1514, doi: 10.1109/PROC.1980.11899.
• [6] J. van den Heuvel, R.A. Leese and M.A. Shepherd, Graph labeling and radio Channel assignment, J. Graph Theory 29 (1998) 263-283, doi: 10.1002/(SICI)1097-0118(199812)29:4<263::AID-JGT5>3.0.CO;2-V
• [7] J. van den Heuvel and S. McGuinness, Coloring the square of a planar graph, J. Graph Theory 42 (2003) 110-124, doi: 10.1002/jgt.10077.
• [8] S. Jendrol' and Z. Skupień, Local structures in plane maps and distance colourings, Discrete Math. 236 (2001) 167-177, doi: 10.1016/S0012-365X(00)00440-4.
• [9] T.R. Jensen and B. Toft, Graph Coloring Problems (John-Wiley & Sons, New York, 1995).
• [10] F. Kramer and H. Kramer, Ein farbungsproblem der knotenpunkte eines graphen bezuglich der distanz, P. Rev. Roumaine Math. Pures Appl. 14 (1969) 1031-1038.
• [11] V.H. MacDonald, The cellular concept, Bell System Technical Journal 58 (1979) 15-41.
• [12] C. McDiarmid and B. Reed, Colouring proximity graphs in the plane, Discrete Math. 199 (1999) 123-137, doi: 10.1016/S0012-365X(98)00292-1.
• [13] A. Sevcíková, Distant Chromatic Number of the Planar Graphs (Manuscript, P.J. Šafárik University, 2001).
• [14] G. Wegner, Graphs with given Diameter and a Colouring Problem (Preprint, University of Dortmund, 1977).
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Bibliografia
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