More Forbidden Minors for Wye-Delta-Wye Reducibility

A graph is Y Y reducible if it can be reduced to isolated vertices by a sequence of series-parallel reductions and Y Y transformations. It is still an open problem to characterize Y Y reducible graphs in terms of a finite set of forbidden minors. We obtain a characterization of such forbidden minors that can be written as clique k-sums for k = 1, 2, 3. As a result we show constructively that the total number of forbidden minors is more than 68 billion up to isomorphism.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Yaming Yu
• Keywords: COMBINATORICS 2006, Forbidden Minors, Open Problem, Series-parallel Reductions