2012/05/01 by Rafayel R. Kamalian, R. R. Kamalian, Kamalian, R. R.
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1205.0130
6 pages, no figures
arxiv created 2012/05/01 · arxiv updated 2012/05/02
A proper edge t-coloring of a graph G 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. An arbitrary nonempty subset of consecutive integers is called an interval. We say that a proper edge t-coloring of a graph G is interval in the vertex x if the spectrum of x is an interval. We say that a proper edge t-coloring φ of a graph G is interval on a subset R0 of vertices of G, if for an arbitrary x∈ R0, φ is interval in x. We say that a subset R of vertices of G has an i-property if there is a proper edge t-coloring of G which is interval on R. If G is a graph, and a subset R of its vertices has an i-property, then the minimum value of t for which there is a proper edge t-coloring of G interval on R is denoted by wR(G). In this paper, for some bipartite graphs, we estimate the value of this parameter in that cases when R coincides with the set of all vertices of one part of the graph.