Abstract
A proper edge t-coloring of a graph G is a coloring of its edges with colors 1,2,???,t such that all colors are used, and no two adjacent edges receive the same color. A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each its vertex x, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers. For an arbitrary simple cycle, all possible values of t are found, for which the graph has a cyclically interval t-coloring.
Highlights
We consider undirected, simple, finite and connected graphs
A proper edge t-coloring of a graph G is a coloring of its edges with colors 1,2,···,t such that all colors are used, and no two adjacent edges receive the same color
A cyclically interval t-coloring of a graph G is a proper edge t-coloring of G such that for each its vertex x, either the set of colors used on edges incident to x or the set of colors not used on edges incident to x forms an interval of integers
Summary
Simple, finite and connected graphs. For a graph G , we denote by V G and E G the sets of its vertices and edges, respectively.An arbitrary nonempty subset of consecutive integers is called an interval. For an arbitrary simple cycle, all possible values of t are found, for which the graph has a cyclically interval t-coloring. For a graph G , we denote by V G and E G the sets of its vertices and edges, respectively. For an arbitrary finite set A , we denote by A the number of elements of A .
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