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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| Materyal Türü: | Journal article |
| Baskı/Yayın Bilgisi: |
Wiley
2018
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| Özet: | 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. |
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