Edge covered critical multigraphs

AbstractLet G be a multigraph with edge set E(G). An edge coloring C of G is called an edge covered coloring, if each color appears at least once at each vertex v∈V(G). The maximum positive integer k such that G has a k edge covered coloring is called the edge covered chromatic index of G and is denoted by χc′(G). A graph G is said to be of class CI if χc′(G)=δ and otherwise of class CII. A pair of vertices {u,v} is said to be critical if χc′(G+uv)>χc′(G). A graph G is said to be edge covered critical if it is of class CII and every edge with vertices in V(G) not belonging to E(G) is critical. Some properties about edge covered critical graphs are considered