An odd hole in a graph is an induced cycle of odd length at least five. In this article we show that every imperfect K 4 -free graph with no odd hole either is one of two basic graphs, or has an even pair or a clique cutset. We use this result to show that every K 4 -free graph with no odd hole has
-free graphs with no odd holes
✍ Scribed by Maria Chudnovsky; Neil Robertson; Paul Seymour; Robin Thomas
- Book ID
- 108167477
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 293 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0095-8956
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📜 SIMILAR VOLUMES
It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). Studying the structure of graphs without odd holes has obvious implications for Berge's strong perfect graph conjecture that states that a g
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