@article{M19circumference3connmaximal1planar,
title = {On the circumference of 3-connected maximal 1-planar graphs},
author = {Mohr, Samuel},
% journal = {},
% number = {3},
pages = {222--223},
% volume = {88},
year = {2019},
url = {http://bgw.labri.fr/2019/booklet.pdf},
biburl = {http://samuel-mohr.de/files/bib/extabstr3.bib},
note = {Bordeaux Graph Workshop 2019},
abstract = {Chen and Yu verified a conjecture of Moon and Moser
that there is a positive constant {$c$} such that the length of a longest cycle of each 3-connected planar graph {$G$} is at least {$c\cdot|V(G)|^{\log_32}$}. \\
A graph is 1-planar if it has a drawing in the plane such that each edge is crossed at most once by another edge and it is maximal 1-planar if it is 1-planar and no edge between non-adjacent vertices can be added to keep its 1-planarity.
We will confirm the results of Moon and Moser and Chen and Yu for the class of maximal 1-planar that a longest cycle of 3-connected maximal 1-planar is at least {$c\cdot|V(G)|^{\log_32}$} and this bound is asymptotically optimal. }
}