Matrix reduction in a combinatorial computation

The 5-flow conjecture of Tutte is that every bridgeless graph has a nowhere-zero 5-flow. Recently Kochol developed a method giving lower bounds for the girth of a smallest counterexample to the 5-flow conjecture. It consists in comparing rank of a matrix with rank of its submatrix. In this paper we present a reduction of the size of these matrices.

Research highlights
► Forbidden configurations for the 5-flow conjecture.
► Transformation of forbidden configurations to vector space.
► Reductions of dimension of vectors using superproper permutations.