Planar graphs and duality

Abstract

We have seen several pairs of different theorems with identical logical structure in Chapter 1. For example, spanning forests (and their complements) were characterized as maximum size subgraphs without containing any circuit (any cut set, respectively). As another example, maximum size collections of linearly independent columns of the circuit matrix (and of the cut set matrix) were shown to be in one-one correspondence with the complements of the spanning forests (with the spanning forests, respectively).