2017/07/04 by Yingzhi Tian, Jixiang Meng, Tian, Yingzhi +5
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1707.01165
openalex publication_date 2017/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [W. Mader, Connectivity keeping paths in k-connected graphs, J. Graph Theory 65 (2010) 61-69.], Mader conjectured that for every positive integer k and every finite tree T with order m, every k-connected, finite graph G with δ(G)≥ \lfloor(3)/(2)k\rfloor+m-1 contains a subtree T' isomorphic to T such that G-V(T') is k-connected. In the same paper, Mader proved that the conjecture is true when T is a path. Diwan and Tholiya [A.A. Diwan, N.P. Tholiya, Non-separating trees in connected graphs, Discrete Math. 309 (2009) 5235-5237.] verified the conjecture when k=1. In this paper, we will prove that Mader's conjecture is true when T is a star or double-star and k=2.