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Counting Gallai 3-colorings of complete graphs
- Publication Year :
- 2018
-
Abstract
- An edge coloring of the n-vertex complete graph K_n is a Gallai coloring if it does not contain any rainbow triangle, that is, a triangle whose edges are colored with three distinct colors. We prove that the number of Gallai colorings of K_n with at most three colors is at most 7(n+1)*2^{n choose 2}, which improves the best known upper bound of \frac{3}{2} * (n-1)! * 2^{(n-1) choose 2} in [Discrete Mathematics, 2017].<br />Comment: 17 pages, 9 pages of appendix, 7 figures
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1805.06805
- Document Type :
- Working Paper