2020/03/05 by Aksoy, Sinan G., Kempton, Mark, Young, Stephen J.
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2003.02393
The cyclic edge-connectivity of a graph G is the least k such that there exists a set of k edges whose removal disconnects G into components where every component contains a cycle. We show that for graphs of minimum degree at least 3 and girth g at least 4, the cyclic edge-connectivity is bounded above by (Δ-2)g where Δ is the maximum degree. We then prove that if the second eigenvalue of the adjacency matrix of a d-regular graph of girth g≥4 is sufficiently small, then the cyclic edge-connectivity is (d-2)g, providing a spectral condition for when this upper bound on cyclic edge-connectivity is tight.