- Publication venue
- Publication date
- 19/02/2024
- Field of study
In this paper, we show that for any positive integer m and kβ[2], let
G be a (2m+2k+2)-connected graph and let a1β,β¦,amβ,s,t be any
distinct vertices of G, there are k internally disjoint s-t paths P1β,β¦,Pkβ in G such that {a1β,β¦,amβ}β©βi=1kβV(Piβ)=β
and Gββi=1kβV(Piβ) 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 eβE(G), and
any distinct vertices a1β,β¦,amβ of GβV(e), there exists a cycle C
in Gβ{a1β,β¦,amβ} such that eβE(C) and GβV(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