The Lower Bound On The Size Of Edge-Coloring Critical Graph & The Fractional Edge Coloring Of Some Graphs

The edge chromatic number x'(G) is the minimum number of colors needed to color the edges of G in such a way that no two adjacent edges are assigned the same color. Vizing's theorem states that for any graph G, x'(G)= or A +1. A graph is said to beclass one if x'(G) = A(G) and class two if x'(G) = A(G)+1. A graph G is critical if G isconnected, and class two and x'(G- e)