English

Connectivity keeping paths in $k$-connected bipartite graphs

Combinatorics 2021-10-05 v3

Abstract

In 2010, Mader [W. Mader, Connectivity keeping paths in kk-connected graphs, J. Graph Theory 65 (2010) 61-69.] proved that every kk-connected graph GG with minimum degree at least 3k2+m1\lfloor\frac{3k}{2}\rfloor+m-1 contains a path PP of order mm such that GV(P)G-V(P) is still kk-connected. In this paper, we consider similar problem for bipartite graphs, and prove that every kk-connected bipartite graph GG with minimum degree at least k+mk+m contains a path PP of order mm such that GV(P)G-V(P) is still kk-connected.

Keywords

Cite

@article{arxiv.2011.03929,
  title  = {Connectivity keeping paths in $k$-connected bipartite graphs},
  author = {Lian Luo and Yingzhi Tian and Liyun Wu},
  journal= {arXiv preprint arXiv:2011.03929},
  year   = {2021}
}
R2 v1 2026-06-23T19:59:22.675Z