Theorem 8.11 : Every 3-regular bridgeless graph contains a 1-factor

(a) Show that Petersen's theorem (Theorem 8.11) can be extended somewhat by proving that if G is a bridgeless graph, every vertex of which has degree 3 or 5 and such that G has at most two vertices of degree 5, then G has a 1-factor. (b) Show that the result in (a) cannot be extended further by giving an example of a bridgeless graph G containing exactly three vertices of degree 5 such that all remaining vertices of G have degree 3 but G has no 1-factor