Towards the Albertson conjecture

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Abstract

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 Kr, the complete graph on r vertices. Albertson, Cranston, and Fox verified the conjecture for r < 12. In this paper we prove it for r < 16.

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Bárat, J., & Tóth, G. (2010). Towards the Albertson conjecture. Electronic Journal of Combinatorics, 17(1), 1–15. https://doi.org/10.37236/345

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