Talk:Pancake graph

Chromatic number of the pancake graph
The upper bounds mentioned in the article are only decent for very small values of $$n$$.

A much better upper bound is the Catlin bound for $$C_4$$-free graphs of roughly $$\frac23n$$ (which is also mentioned in Elena's paper, but apparently did not make it to the WIKI).

Since $$\chi(P_n)$$ is subadditive (https://math.stackexchange.com/questions/3057032/chromatic-number-of-the-pancake-graph-is-subadditive) and $$\chi(P_7)=4$$ an even better upper bound is given by $$\chi(P_n)\leq\frac{4n+4}7$$.

(Note: I do not intend to make an effort to publish the stackexchange result, otherwise I would have modified the main page, but that is probably not allowed with "unofficial" results)

--Leen Droogendijk (talk) 09:36, 3 January 2019 (UTC)