@article{LUO2022, 
author = {Lian LUO and Yingzhi TIAN},
title = {On the Connectivity Keeping some Trees in Connected and 2-Connected Bipartite Graphs},
year = {2022},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {39},
number = {3},
pages = {283-286},
keywords = {Connectivity, Caterpillars, Stars, Double-stars, Bipartite graphs},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2021.03.24.0001},
doi = {10.13568/j.cnki.651094.651316.2021.03.24.0001},
abstract = {In 2010, Mader conjectured that for any tree T of order m, every k-connected graph G with minimum degree at least  ⌊3k2⌋+m-1 contains a subtree  T′≅T such that G−V(T′) is still k-connected. For bipartite graphs, we proposed a similar conjecture as follows: for every positive integer k and every finite tree T with bipartition X and Y (denote t = max{|X|, |Y|}), every k-connected bipartite graph G with minimum degree at least k+t contains a subtree  T′≅T such that G−V (T′) is still k-connected. In this paper, we confirm this conjecture for all caterpillars whose internal vertices is at most 3 when k=1 and k=2.}
}