A triangle-free circle graph with chromatic number 5

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Abstract

It follows from the results of Karapetyan (1984), Gyárfás and Lehel (1985), and Kostochka (1988) that 4 ≤ χ* ≤ 5 where χ* = max{χ(G): G is a triangle-free circle graph}. We show that χ* ≥ 5 and thus χ* = 5. This disproves the conjecture of Karapetyan that χ* = 4 and answers negatively a question of Gyárfaχ*s and Lehel.

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APA

Ageev, A. A. (1996). A triangle-free circle graph with chromatic number 5. Discrete Mathematics, 152(1–3), 295–298. https://doi.org/10.1016/0012-365X(95)00349-2

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