Interval edge-colorings of complete graphs
Hrant H. Khachatrian, Petros A. Petrosyan

TL;DR
This paper investigates interval edge-colorings of complete graphs, disproves a previous conjecture, and provides new bounds and exact values for the maximum number of colors used in such colorings.
Contribution
It introduces a new construction technique based on 1-factorizations, refutes a conjecture, and determines exact values of W(K_{2n}) for n ≤ 12.
Findings
Disproved the existing conjecture on W(K_{2n})
Improved bounds on W(K_{2n})
Determined exact W(K_{2n}) for n ≤ 12
Abstract
An edge-coloring of a graph with colors is an interval -coloring if all colors are used, and the colors of edges incident to each vertex of are distinct and form an interval of integers. A graph is interval colorable if it has an interval -coloring for some positive integer . For an interval colorable graph , denotes the greatest value of for which has an interval -coloring. It is known that the complete graph is interval colorable if and only if the number of its vertices is even. However, the exact value of is known only for . The second author showed that if , where is odd and is nonnegative, then . Later, he conjectured that if , then , where $\left \| n_2 \right…
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 · graph theory and CDMA systems
