Connectivity and β-invariants of isotropic systems and 4-regular graphs Original Research Article

For every matroid M, H. Crapo defined an invariant β(M) which reflects some connectivity properties of M. We adapt the definition of this invariant to isotropic systems. As an application we study the properties of an invariant β4(H) defined by P. Martin for any 4-regular graph H, and we show that β4(H) is related with the cyclic edge-connectivity of H.