One-sided interval edge-colorings of bipartite graphs

On one-sided interval edge colorings of biregular bipartite graphs

A proper edge t-coloring of a graphG is a coloring of edges of G with colors 1, 2, . . . , t such that all colors are used, and no two adjacent edges receive the same color. The set of colors of edges incident with a vertex x is called a spectrum of x. Any nonempty subset of consecutive integers is called an interval. A proper edge t-coloring of a graph G is interval in the vertex x if the spec...

On interval edge-colorings of bipartite graphs of small order

An edge-coloring of a graph G with colors 1, . . . , t is an interval t-coloring if all colors are used, and the colors of edges incident to each 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 problem of deciding whether a bipartite graph is interval colorable is NP-complete. The smalle...

Edge Colorings in Bipartite Graphs

On interval total colorings of bipartite graphs

An interval total t coloring of a graph G is a total coloring of with colors 1, such that at least one vertex or edge of is colored by color − G 2, , t ... G , 1, 2, , i i t = ... , and the edges incident to each vertex together with are colored by consecutive colors, where is the degree of the vertex in . In this paper interval total colorings of bipartite graphs are investigated. ( ) v V G ∈

Interval Total Colorings of Bipartite Graphs

A total coloring of a graph G is a coloring of its vertices and edges such that no adjacent vertices, edges, and no incident vertices and edges obtain the same color. The concept of total coloring was introduced by V. Vizing [15] and independently by M. Behzad [3]. The total chromatic number χ (G) is the smallest number of colors needed for total coloring of G. In 1965 V. Vizing and M. Behzad c...