Article contents
Scott's Induced Subdivision Conjecture for Maximal Triangle-Free Graphs
Published online by Cambridge University Press: 21 March 2012
Abstract
Scott conjectured in [6] that the class of graphs with no induced subdivision of a given graph is χ-bounded. We verify his conjecture for maximal triangle-free graphs.
Keywords
- Type
- Paper
- Information
- Copyright
- Copyright © Cambridge University Press 2012
References
[1]Bollobás, B. and Thomason, A. (1998) Proof of a conjecture of Mader, Erdős and Hajnal on topological complete subgraphs. Europ. J. Combin. 19 883–887.CrossRefGoogle Scholar
[2]Ding, G., Seymour, P. and Winkler, P. (1994) Bounding the vertex cover number of a hypergraph. Combinatorica 14 23–34.CrossRefGoogle Scholar
[3]Gyárfás, A. (1987) Problems from the world surrounding perfect graphs. Zastos. Mat. XIX 413–441.Google Scholar
[4]Kim, J. (1995) The Ramsey number R(3, t) has order of magnitude t 2/log (t). Random Struct. Alg. 7 173–207.CrossRefGoogle Scholar
[5]Mader, W. (1967) Homomorphieeigenschaften und mittlere Kantendichte von Graphen. Mathematische Annalen 174 265–268.CrossRefGoogle Scholar
[6]Scott, A. (1997) Induced trees in graphs of large chromatic number. J. Graph Theory 24 297–311.3.0.CO;2-J>CrossRefGoogle Scholar
- 3
- Cited by