Contract grant sponsor: NSF; Contract grant numbers: IIS-1117631; DMS-1001091 (M.C.); Contract grant sponsor: NSF; Contract grant number: DMS-1001091 (M.P.).
The Structure of Claw-Free Perfect Graphs
Article first published online: 11 MAR 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 3, pages 203–230, March 2014
How to Cite
Chudnovsky, M. and Plumettaz, M. (2014), The Structure of Claw-Free Perfect Graphs. J. Graph Theory, 75: 203–230. doi: 10.1002/jgt.21732
- Issue published online: 6 JAN 2014
- Article first published online: 11 MAR 2013
- Manuscript Revised: 27 DEC 2012
- Manuscript Received: 29 OCT 2011
- NSF. Grant Numbers: IIS-1117631, DMS-1001091 (M.C.)
- NSF. Grant Number: DMS-1001091 (M.P.)
- graph structure;
- quasi-line graph
In 1988, Chvátal and Sbihi (J Combin Theory Ser B 44(2) (1988), 154–176) proved a decomposition theorem for claw-free perfect graphs. They showed that claw-free perfect graphs either have a clique-cutset or come from two basic classes of graphs called elementary and peculiar graphs. In 1999, Maffray and Reed (J Combin Theory Ser B 75(1) (1999), 134–156) successfully described how elementary graphs can be built using line-graphs of bipartite graphs using local augmentation. However, gluing two claw-free perfect graphs on a clique does not necessarily produce claw-free graphs. In this article, we give a complete structural description of claw-free perfect graphs. We also give a construction for all perfect circular interval graphs.