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 ${\frac {2}{3}}n$ (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)