Bad news for chordal partitions

Reed and Seymour [1998] asked whether every graph has a partition into induced connected non-empty 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 an...

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Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Scott, A, Seymour, P, Wood, D
Μορφή: Journal article
Έκδοση: Wiley 2018
Περιγραφή
Περίληψη:Reed and Seymour [1998] asked whether every graph has a partition into induced connected non-empty 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.