Characterizing almost-median graphs

Boštjan Brešar
2007 European journal of combinatorics (Print)  
Almost-median and semi-median graphs are two natural generalizations of the well-known class of median graphs. In this note we prove that a semi-median graph is almost-median if and only if it does not contain any convex cycle of length greater than four.
doi:10.1016/j.ejc.2005.10.009 fatcat:r3qwgkaxdbd2fa7xsldsbxgdte