- Abstract:
-
Gyárfás conjectured in 1985 that for all k, ℓ, every graph with no clique of size more than k and no odd hole of length more than ℓ has chromatic number bounded by a function of k, ℓ. We prove three weaker statements:. •Every triangle-free graph with sufficiently large chromatic number has an odd hole of length different from five;•For all ℓ, every triangle-free graph with sufficiently large chromatic number contains either a 5-hole or an odd hole of length more than ℓ•For all k, ℓ, every gra...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Version:
- Accepted manuscript
- Files:
-
-
(pdf, 267.0KB)
-
- Publisher copy:
- 10.1016/j.jctb.2016.01.003
-
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- Publisher:
- Elsevier B.V. Publisher's website
- Journal:
- Journal of Combinatorial Theory, Series B Journal website
- Volume:
- 118
- Pages:
- 109-128
- Chapter number:
- C
- Publication date:
- 2016-01-27
- Acceptance date:
- 2015-08-28
- DOI:
- EISSN:
-
1096-0902
- ISSN:
-
0095-8956
- URN:
-
uuid:91edfafa-aecb-47da-a3fe-36b1d7d70f35
- Source identifiers:
-
604679
- Local pid:
- pubs:604679
- Keywords:
- Copyright holder:
- Elsevier B.V.
- Copyright date:
- 2016
- Notes:
- This is an accepted manuscript of a journal article published by Elsevier in Journal of Combinatorial Theory, Series B on 2015-01-27, available online: http://dx.doi.org/10.1016/j.jctb.2016.01.003
Journal article
Induced subgraphs of graphs with large chromatic number. II. Three steps towards Gyarfas' conjectures
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