
TL;DR
This paper characterizes the possible numbers of colors for proper edge colorings of simple cycles where adjacent edges are colored with consecutive or wrap-around colors, expanding understanding of cycle colorings.
Contribution
It determines all feasible color counts for proper edge colorings of simple cycles with specific adjacency color constraints.
Findings
Identifies all t for which such colorings exist for C(n)
Provides a complete characterization of these colorings for all n≥3
Enhances understanding of cycle edge coloring constraints
Abstract
A proper edge -coloring of a graph is a coloring of its edges with colors such that all colors are used, and no two adjacent edges receive the same color. For any integer , all possible values of are found, for which there exists such a proper edge -coloring of the simple cycle C(n), which uses for each pair of adjacent edges either consecutive colors or the first and the last ones.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research
