Question: Recall that a matching in G is a sub graph with all vertices of degree 1 and that a perfect matching is a sub graph with all vertices of degree 1 that includes all vertices of G.
(a) Find as many different perfect matchings as you can in a 6-cycle graph.
(b) Find as many different perfect matchings as you can in K4.
(c) Create a 4-regular planar graph and properly edge-color it.
(d) How does the concept of perfect matchings relate to edge coloring of k-regular graphs?