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For paths Pₙ, G. Chartrand, L. Nebeský and P. Zhang showed that $ac'(Pₙ) ≤ \binom{n-2}{2} + 2$ for every positive integer n, where ac'(Pₙ) denotes the nearly antipodal chromatic number of Pₙ. In this paper we show that $ac'(Pₙ) ≤ \binom{n-2}{2} - n/2 - ⎣10/n⎦ + 7$ if n is even positive integer and n ≥ 10, and $ac'(Pₙ) ≤ \binom{n-2}{2} - (n-1)/2 - ⎣13/n⎦ + 8$ if n is odd positive integer and n ≥ 13. For all even positive integers n ≥ 10 and all odd positive integers n ≥ 13, these results improve the upper bounds for nearly antipodal chromatic number of Pₙ.
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Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
159-174
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-02-21
poprawiono
2006-10-31
Twórcy
autor
- Department of Mathematics and Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, P.R. China
autor
- Department of Mathematics and Physics, Hebei Normal University of Science and Technology, Qinhuangdao 066004, P.R. China
autor
- Applied Mathematics Institute, Hebei University of Technology, Tianjin 300130, P.R. China
Bibliografia
- [1] G. Chartrand, D. Erwin, F. Harary and P. Zhang, Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001) 77-85.
- [2] G. Chartrand, D. Erwin and P. Zhang, A graph labeling problem suggested by FM channel restrictions, Bull. Inst. Combin. Appl. 43 (2005) 43-57.
- [3] G. Chartrand, D. Erwin and P. Zhang, Radio antipodal colorings of graphs, Math. Bohem. 127 (2002) 57-69.
- [4] G. Chartrand, L. Nebeský and P. Zhang, Radio k-colorings of paths, Discuss. Math. Graph Theory 24 (2004) 5-21, doi: 10.7151/dmgt.1209.
- [5] D. Fotakis, G. Pantziou, G. Pentaris and P. Spirakis, Frequency assignment in mobile and radio networks, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 45 (1999) 73-90.
- [6] R. Khennoufa and O. Togni, A note on radio antipodal colorings of paths, Math. Bohem. 130 (2005) 277-282.
- [7] 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
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1352