The diameter of modular flip-graphs for non-orientable filling surfaces lies between 5n/2 and 4n asymptotically, and equals 5n/2 for the Möbius strip.
A logarithmic bound for the chromatic number of the associahedron
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abstract
We show that the chromatic number of the $n$-dimensional associahedron grows at most logarithmically with $n$, improving a bound from and proving a conjecture of Fabila-Monroy et al. (2009).
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Flip-graphs of non-orientable filling surfaces
The diameter of modular flip-graphs for non-orientable filling surfaces lies between 5n/2 and 4n asymptotically, and equals 5n/2 for the Möbius strip.