Bridged graph

Bridged graph --- граф с мостами.

A graph [math]\displaystyle{ G }[/math] is a bridged graph if each cycle [math]\displaystyle{ C }[/math] of length at least 4 contains two vertices whose distance from each other in [math]\displaystyle{ G }[/math] is strictly less than that in [math]\displaystyle{ C }[/math]. A graph is called bridged if every cycle of length at least 4 has a bridge. Observe that in a bridged graph every cycle of length 4 or 5 has a chord. Bridged graphs are in general not perfect, as the wheel [math]\displaystyle{ W_{7} }[/math] shows.