Edge Cover Coloring And Fractional Edge Coloring Of Graphs

The coloring theory of graphs is one important branch of graph theory. The coloring theory has many kinds, such as edge coloring, vertex coloring, face coloring, total coloring and so on. Among them, the edge coloring is given most attention and has many perfect results. The proper edge coloring is to divide the edge set of G into some dijoint independent edge sets. In proper edge coloring theory, it is well known that Vizing's Theorem and the classification problem. Recently, many authors consider the generalization of proper edge coloring, that is, we can consider other forms in which we can divide the edge set. The aim of this thesis is to discuss some topics on edge coloring problems such as edge cover coloring, f-edge cover coloring, fractional edge cover cloring and fractional edge coloring of graphs.Let G(V, E) be a graph with vertex set V and edge set E. If 5 is a set, we shall denote by \S\ the cardinality of 5. Throughout this thesis the term graph is used to denote a simple graph G with finite vertex set V and a finite edge set E. If multiple edges are allowed, G is called a multigraph. For a vertex v of G, the degree of v in G is denoted by d_c(v). Let N_G(v) denote the set of neighbors of vertex v. Set δ(G) = min{d_G(v) : v (?) V(G)}, the minimum degree of G, and â–³(G) = max{d_G{v) : v (?) V(G)}, the maximum degree of G. If there is no confusion, we use V, E, N(v), δ, A instead of V(G), E(G), N_G(v), δ(G), A(G), respectively.Let G_δ denote the subgraph of G induced by the vertices of degree S. G is regular if â–³(G) = δ(G) = d, we also say that G is d-regular. A graph is cubic if it is 3-regular. A graph G is bipartite if there exists a partition (V₁. V₂) of V(G)...