Back to Search
Start Over
Proper Distinguishing Colorings with Few Colors for Graphs with Girth at Least 5
- Source :
- Electronic Journal of Combinatorics. Vol. 25(3), 2018, #P3.5
- Publication Year :
- 2017
-
Abstract
- The distinguishing chromatic number, $\chi_D(G)$, of a graph $G$ is the smallest number of colors in a proper coloring, $\varphi$, of $G$, such that the only automorphism of $G$ that preserves all colors of $\varphi$ is the identity map. Collins and Trenk conjectured that if $G$ is connected with girth at least 5 and $G\ne C_6$, then $\chi_D(G)\le \Delta+1$. We prove this conjecture.<br />Comment: 9 pages, 3 figures; expanded introduction and bibliography from version 1
- Subjects :
- Mathematics - Combinatorics
05C15, 05C25
Subjects
Details
- Database :
- arXiv
- Journal :
- Electronic Journal of Combinatorics. Vol. 25(3), 2018, #P3.5
- Publication Type :
- Report
- Accession number :
- edsarx.1707.05439
- Document Type :
- Working Paper