2012/05/01 by Rafael R. Kamalian, R. R. Kamalian, Kamalian, R. R.
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1205.0131
10 pages, no figures
arxiv created 2012/05/01 · openalex publication_date 2012/05/01 · arxiv updated 2012/05/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A proper edge t-coloring of a graph G is a coloring of edges of G with colors 1,2,...,t such that each of t colors is used, and adjacent edges are colored differently. The set of colors of edges incident with a vertex x of G is called a spectrum of x. A proper edge t-coloring of a graph G is interval for its vertex x if the spectrum of x is an interval of integers. A proper edge t-coloring of a graph G is persistent-interval for its vertex x if the spectrum of x is an interval of integers beginning from the color 1. For graphs G from some classes of graphs, we obtain estimates for the possible number of vertices for which a proper edge t-coloring of G can be interval or persistent-interval.