modular edge colorings of mycielskian graphs

Mi-Edge Colorings of Graphs

An edge coloring of a graph G is called Mi-edge coloring if at most i colors appear at any vertex of G. Let Ki(G) denote the maximum number of colors used in an Mi-edge coloring of G. In this paper we determine the exact value of K2(G) for any graph G of maximum degree at most 3. Mathematics Subject Classification: 05C15, 05C38

Acyclic edge colorings of graphs

A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an acyclic edge coloring of G. For certain graphs G, a′(G) ≥ ∆(G) + 2 where ∆(G) is the maximum degree in G. It is known that a′(G) ≤ 16∆(G) for any graph G (see [2],[10]). We prove that there exists a const...

Edge Colorings in Bipartite Graphs

Interval edge-colorings of composition of graphs

An edge-coloring of a graph G with consecutive integers c1, . . . , ct is called an interval t-coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. The set of all interval colorable graphs is denoted by N. In 2004, Giaro and...

Edge colorings and total colorings of integer distance graphs

On list edge-colorings of subcubic graphs

In this paper we study list edge-colorings of graphs with small maximal degree. In particular, we show that simple subcubic graphs are '10/3-edge choosable'. The precise meaning of this statement is that no matter how we prescribe arbitrary lists of three colors on edges of a subgraph H of G such that A(H)~< 2, and prescribe lists of four colors on E(G)\E(H), the subcubic graph G will have an e...