Interval edge colorings of some products of graphs
Petros A. Petrosyan

TL;DR
This paper investigates the conditions under which various graph products preserve the property of having an interval edge coloring, extending previous results and introducing new classes of such graphs.
Contribution
It proves that certain graph products, including lexicographic, strong, and tensor products, preserve interval colorability under specified conditions.
Findings
Cartesian product of interval colorable graphs remains interval colorable.
Lexicographic and strong products are interval colorable if one factor is regular.
Tensor and strong tensor products are interval colorable when one graph is regular.
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. A graph is interval colorable, if there is an integer for which has an interval -coloring. Let be the set of all interval colorable graphs. In 2004 Kubale and Giaro showed that if , then the Cartesian product of these graphs belongs to . Also, they formulated a similar problem for the lexicographic product as an open problem. In this paper we first show that if , then for any . Furthermore, we show that if and is a regular graph, then strong and…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Limits and Structures in Graph Theory
