Vertices of degree 6 in a contraction critically 6-connected graph Original Research Article

An edge of a 6-connected graph is said to be 6-contractible if the contraction of the edge results in a 6-connected graph. A contraction critically 6-connected graph is a 6-connected graph with no 6-contractible edge. We prove that each contraction critically 6-connected graph G has at least 17|V(G)| vertices of degree 6.