Face extensions in planar cubic graphs Original Research Article

A planar cubic graph is k-extendable, k ≥4, if it can be obtained from the cube by repeatedly choosing two edges lying on a common face of length at most k, subdividing them once and joining the resulting degree two vertices. It turns out that every cyclically 4-edge connected planar cubic graph is 7-extendable. For each k ϵ {4,5,6,7}, we study k-extendable graphs in terms of excluded minors.