Tiled partial cubes

Bo?tjan Bre?ar, Wilfried Imrich, Sandi Klav?ar, Henry Martyn Mulder, Riste ?krekovski
2002 Journal of Graph Theory  
In the quest to better understand the connection between median graphs, trianglefree graphs and partial cubes, a hierarchy of subclasses of partial cubes has been introduced. In this paper we study the role of tiled partial cubes in this scheme. For instance, we prove that almost-median graphs are tiled and that tiled partial cubes are semi-median. We also describe median graphs as tiled partial cubes without convex Q − 3 and extend an inequality for median graphs to a larger subclass of partial cubes.
doi:10.1002/jgt.10031 fatcat:n7dh5tzx6zaflkeb5ay5opsbxu