Yota Otachi, Koichi Yamazaki. A lower bound for the vertex boundary-width of complete k-ary trees. Discrete Mathematics, 308(12):2389-2395, 2008. [doi]
@article{OtachiY08,
title = {A lower bound for the vertex boundary-width of complete k-ary trees},
author = {Yota Otachi and Koichi Yamazaki},
year = {2008},
doi = {10.1016/j.disc.2007.05.014},
url = {http://dx.doi.org/10.1016/j.disc.2007.05.014},
tags = {completeness},
researchr = {https://researchr.org/publication/OtachiY08},
cites = {0},
citedby = {0},
journal = {Discrete Mathematics},
volume = {308},
number = {12},
pages = {2389-2395},
}