Estimates for the number of vertices with an interval spectrum in proper edge colorings of some graphs [article]

R.R. Kamalian
2012 arXiv   pre-print
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
more » ... ing 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.
arXiv:1205.0131v1 fatcat:jz5i3ltzbjabhp2gmaekbjim3y