On a Generalization of Interval Edge Colorings of Graphs
Abstract
An interval edge (t; h) – coloring (h 2 Z+) of a graph G is a proper coloring α of edges of G with colors 1, 2..., t such that at least one edge of G is colored by i; i = 1, 2..., t and the colors of edges incident with each vertex v satisfy the condition dG(v) – 1≤ max S (v, α) – min S (v, α)≤dG (v) + h – 1, where dG(v) is the degree of a vertex v and S (v, α) is the set of colors of edges incident with v. In this paper we investigate some properties of interval edge (t; h) – colorings.
References
A.S. Asratian, R.R. Kamalian, Interval colorings of edges of amultigraph, Appl. Math. 5 (1987), Yerevan State University, pp. 25-34.
R.R. Kamalian, Interval Edge Colorings of Graphs, Doctoral dissertation, The Institute of Mathematics of the Siberian Branch of the Academy of Sciences of USSR, Novosibirsk, 1990.
F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
V.G. Vizing, The chromatic index of amultigraph, Kibernetika 3 (1965), pp. 29-39.
D.B. West, Introduction to Graph Theory, Prentice-Hall, NewJersey, 2001.
R.R. Kamalian, Interval colorings of complete bipartite graphs and trees, Preprint of the Computing Centre of the Academy of Sciences of Armenia, 1989, 11p.
Downloads
Published
How to Cite
Issue
Section
License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.