Removable edges in cyclically 4-edge-connected cubic graphs
\textit{N. C. Wormald} [Combinatorial mathematics VI, Proc. Conf., Armidale/Aust. 1978, Lect. Notes Math. 748, 199-206 (1979; Zbl 0414.05034)] showed that any cyclically 4-edge-connected cubic graph with at least 10 vertices has an edge e such that the graph obtained from G by removing e, this is deleting e and suppressing the two vertices of degree 2 created by the deletion, is also cyclically 4-edge connected. The main result of this paper is: Any cyclically 4-edge-connected cubic graph G with at least 12 vertices has at least \((| E(G)| +12)/5\) removable edges. The authors also prove that this result is best possible for the class of all cyclically 4-edge-connected cubic graphs by determining the extreme graphs.
scientific article; zbMATH DE number 4047768