Towards The Albertson Conjecture
Abstract
Albertson conjectured that if a graph $G$ has chromatic number $r$ then its crossing number is at least as much as the crossing number of $K_r$. Albertson, Cranston, and Fox verified the conjecture for $r\le 12$. We prove the statement for $r\le 16$.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2009
- DOI:
- 10.48550/arXiv.0909.0413
- arXiv:
- arXiv:0909.0413
- Bibcode:
- 2009arXiv0909.0413B
- Keywords:
-
- Mathematics - Combinatorics;
- 05C10;
- 05C15
- E-Print:
- 13 pages, 4 figures