Erik Kuo, on his article about graphical condensation proved the following theorems:
Theorem 1
Let G=(V1,V2,E) be
a weighted planar bipartite graph in which |V1|=|V2|. Let vertices a,b,c
and d appear on a face of G, in that order. If a,c belong to V1, and b,d
belong to V2, then:
Theorem 2
Let G=(V1,V2,E) be
a weighted planar bipartite graph in which |V1|=|V2|. Let vertices a,b,c
and d appear on a face of G, in that order. If a,b belong to V1, and c,d
belong to V2, then:
