I've been taught in lecture last week about graph planarity testing. But the main idea of conflict bridges I still don't understand. Then I search online, from wikipedia to mathworld, there are nothing about this bridge concept. I begin to wonder if this idea is a standard method to do this kind of testing. Are these definitions look familiar to you? Could you give me a reference where it's from? H-bridges: if H is a subgraph of G, an H-bridge of G is either: 1. an dege not in H whose endvertices are in H, or 2. a component of G-V(H) together with the edges ( and vertices of attachment) that connect it to H. Conflicting Bridges Given a cycle H in graph G, two H-bridges A, B conflict if they have three common vertices of attchment or there are four vertices v1 v2 v3 v4 in cyclic order on H such that v1 v3 are vertices of attachment of A and v2 v4 are vertices of attchment of B. Planarity testing Suppose Gis not a tree. Let H be a cycle in G: 1 if any H-bridge of G is non-planar the G is non-planar. 1 if three H-bridges of G mutually conflict, then G is non-planar. At last, if you are my lecturor, and think I plagiarized your lecture notes, please PM me.