Geodesic
Towards the Albertson conjecture
The electronic journal of combinatorics, Tome 17 (2010)
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Albertson conjectured that if a graph $G$ has chromatic number $r$, then the crossing number of $G$ is at least as large as the crossing number of $K_r$, the complete graph on $r$ vertices. Albertson, Cranston, and Fox verified the conjecture for $r\le 12$. In this paper we prove it for $r\le 16$.
DOI : 10.37236/345
Classification : 05C10, 05C15
Mots-clés : chromatic number, crossing number 
@article{10_37236_345,
     author = {J\'anos Bar\'at and G\'eza T\'oth},
     title = {Towards the {Albertson} conjecture},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/345},
     zbl = {1188.05051},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/345/}
}
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János Barát; Géza Tóth. Towards the Albertson conjecture. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/345

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