A note on interval edge-colorings of graphs
R.R. Kamalian, P.A. Petrosyan

TL;DR
This paper investigates the bounds on the number of colors used in interval edge-colorings of connected graphs, establishing upper limits based on graph properties such as connectivity and regularity.
Contribution
It proves new upper bounds for the number of colors in interval edge-colorings of connected graphs, improving previous bounds for regular graphs with certain size conditions.
Findings
For connected graphs, t ≤ 2n - 3.
For connected r-regular graphs with n ≥ 2r + 2, t ≤ 2n - 5.
Provides theoretical bounds on interval edge-colorings.
Abstract
An edge-coloring of a graph with colors is called an interval -coloring if for each there is at least one edge of colored by , and the colors of edges incident to any vertex of are distinct and form an interval of integers. In this paper we prove that if a connected graph with vertices admits an interval -coloring, then . We also show that if is a connected -regular graph with vertices has an interval -coloring and , then this upper bound can be improved to .
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Limits and Structures in Graph Theory
