Issue |
RAIRO-Theor. Inf. Appl.
Volume 49, Number 1, January-March 2015
|
|
---|---|---|
Page(s) | 47 - 60 | |
DOI | https://doi.org/10.1051/ita/2014027 | |
Published online | 18 February 2015 |
New bounds on the edge-bandwidth of triangular grids∗
1
School of Electronics and Information Engineering, Tongji
University, Shanghai
200092, P.R.
China.
linlan@tongji.edu.cn
2
The Key Laboratory of Embedded System and Service Computing,
Ministry of Education, Tongji University, Shanghai
200092, P.R.
China.
3
Department of Mathematics, Zhengzhou University,
Zhengzhou
450001, P.R.
China.
linyixun@zzu.edu.cn
Received: 23 March 2014
Accepted: 8 October 2014
The edge-bandwidth of a graph G is the bandwidth of the line graph of G. Determining the edge-bandwidth B′(Tn) of triangular grids Tn is an open problem posed in 2006. Previously, an upper bound and an asymptotic lower bound were found to be 3n − 1 and 3n − o(n) respectively. In this paper we provide a lower bound 3n − ⌈ n/ 2 ⌉ and show that it gives the exact values of B′(Tn) for 1 ≤ n ≤ 8 and n = 10. Also, we show the upper bound 3n − 5 for n ≥ 10.
Mathematics Subject Classification: 05C78 / 68M10 / 68R10
Key words: Bandwidth / edge-bandwidth / triangular grid / lower bound / upper bound
© EDP Sciences 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.