Abstract
An edge of ak-connected graph is said to bek-contractible if the contraction of the edge results in ak-connected graph. We prove that every triangle-freek-connected graphG has an induced cycleC such that all edges ofC arek-contractible and such thatG−V(C) is (k−3)-connected (k≥4). This result unifies two theorems by Thomassen [5] and Egawa et. al. [3].
Similar content being viewed by others
References
G. Chartrand, andL. Lesniak:Graphs and Digraphs, Second edition, Wadsworth, Belmont, CA (1986).
N. Dean: Distribution of contractible edges ink-connected graphs,preprint.
Y. Egawa, H. Enomoto, andA. Saito: Contractible edges in triangle-free graphs,Combinatorica 6 (1986) 269–274.
W. Mader: Generalization of critical connectivity of graphs,Discrete Math. 72 (1988) 267–283.
C. Thomassen: Nonseparating cycles ink-connected graphs,J. Graph Theory 5 (1981) 351–354.
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Toshiro Tsuzuku on his sixtieth birthday