Location of Repository

Computing sharp 2-factors in claw-free graphs.\ud

By H.J. Broersma and Daniel Paulusma


In a previous paper we obtained an upper bound for the minimum number of components of a 2-factor in a claw-free graph. This bound is sharp in the sense that there exist infinitely many claw-free graphs for which the bound is tight. In this paper we extend these results by presenting a polynomial algorithm that constructs a 2-factor of a claw-free graph with minimum degree at least four whose number of components meets this bound. As a byproduct we show that the problem of obtaining a minimum 2-factor (if it exists) is polynomially solvable for a subclass of claw-free graphs. As another byproduct we give a short constructive proof for a result of Ryjáček, Saito and Schelp.\ud \u

Topics: Claw-free graph, 2-factor, Number of components, Polynomial algorithm.
Publisher: Elsevier
Year: 2010
DOI identifier: 10.1016/j.jda.2009.07.001
OAI identifier: oai:dro.dur.ac.uk.OAI2:7418

Suggested articles



  1. (1973). A maxfm;ng algorithm for determining the graph H from its line graph doi
  2. (1999). A note on cycles in 2-factors of line graphs,
  3. (1998). Closure concepts for claw-free graphs, doi
  4. (1999). Closure, 2-factor, and cycle coverings in claw-free graphs,
  5. (2007). Even subgraphs of bridgeless graphs and 2-factors of line graphs, doi
  6. (2007). Graph factors and factorization: 1985-2003: A survey, doi
  7. (1969). Graph Theory, Addison-Wesley,
  8. (2000). Graph Theory, Second edition, Graduate Texts in Mathematics 173,
  9. (1984). Hamiltonian results in K1;3-free graphs, doi
  10. (1999). On 2-factors in claw-free graphs, doi
  11. (1997). On a closure concept in claw-free graphs,
  12. (2007). On the number of components in a 2-factor of a claw-free graph, doi
  13. (2004). On traceability and 2-factors in claw-free graphs,
  14. (1991). Regular factors in K1;3-free graphs, doi
  15. (1991). Regular factors in K1;n-free graphs, doi
  16. (1997). Ryja´cˇek Claw-free graphs—a survey,
  17. Sharp upper bounds for the minimum number of components of 2-factors in claw-free graphs, doi
  18. (2001). Two-factors with few cycles in claw-free graphs, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.