- Publication venue
- Publication date
- 19/02/2024
- Field of study
In this paper, we show that for any positive integer m and k∈[2], let
G be a (2m+2k+2)-connected graph and let a1​,…,am​,s,t be any
distinct vertices of G, there are k internally disjoint s-t paths P1​,…,Pk​ in G such that {a1​,…,am​}∩⋃i=1k​V(Pi​)=∅ and G−⋃i=1k​V(Pi​) is 2-connected, which
generalizes the result by Chen, Gould and Yu [Combinatorica 23 (2003)
185--203], and Kriesell [J. Graph Theory 36 (2001) 52--58]. The case k=1
implies that for any (2m+5)-connected graph G, any edge e∈E(G), and
any distinct vertices a1​,…,am​ of G−V(e), there exists a cycle C
in G−{a1​,…,am​} such that e∈E(C) and G−V(C) is
2-connected, which improves the bound 10m+11 of Y. Hong, L. Kang and X. Yu in
[J. Graph Theory 80 (2015) 253--267].Comment: 10 page - Publication venue
- 'Elsevier BV'
- Publication date
- Field of study
- Publication venue
- 'Elsevier BV'
- Publication date
- Field of study