Reed and Seymour  asked whether every graph has a partition into induced connected nonempty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is “no.” In fact, we show that the answer is still “no” for several relaxations of the question.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Hadwiger's conjecture
- chordal partition