ArticleOriginal scientific text

Title

On k-factor-critical graphs

Authors

Abstract

A graph is said to be k-factor-critical if the removal of any set of k vertices results in a graph with a perfect matching. We study some properties of k-factor-critical graphs and show that many results on q-extendable graphs can be improved using this concept.

Keywords

matching, extendable, factor

Bibliography

  1. V. N. Bhat and S. F. Kapoor, The Powers of a Connected Graph are Highly Hamiltonian, Journal of Research of the National Bureau of Standards, Section B 75 (1971) 63-66.
  2. G. Chartrand, S. F. Kapoor and D. R. Lick, n-Hamiltonian Graphs, J. Combin. Theory 9 (1970) 308-312, doi: 10.1016/S0021-9800(70)80069-2.
  3. O. Favaron, Stabilité, domination, irredondance et autres parametres de graphes, These d'Etat, Université de Paris-Sud, 1986.
  4. O. Favaron, E. Flandrin and Z. Ryjáek, Factor-criticality and matching extension in DCT-graphs, Preprint.
  5. T. Gallai, Neuer Beweis eines Tutte'schen Satzes, Magyar Tud. Akad. Mat. Kutató Int. Közl. 8 (1963) 135-139.
  6. L. Lovász, On the structure of factorizable graphs, Acta Math. Acad. Sci. Hungar. 23 (1972) 179-195, doi: 10.1007/BF01889914.
  7. L. Lovász and M. D. Plummer, Matching Theory, Annals of Discrete Math. 29 (1986).
  8. M. Paoli, W. W. Wong and C. K. Wong, Minimum k-Hamiltonian Graphs II, J. Graph Theory 10 (1986) 79-95, doi: 10.1002/jgt.3190100111.
  9. M. D. Plummer, On n-extendable graphs, Discrete Math. 31 (1980) 201-210, doi: 10.1016/0012-365X(80)90037-0.
  10. M. D. Plummer, Toughness and matching extension in graphs, Discrete Math. 72 (1988) 311-320, doi: 10.1016/0012-365X(88)90221-X.
  11. M. D. Plummer, Degree sums, neighborhood unions and matching extension in graphs, in: R. Bodendiek, ed., Contemporary Methods in Graph Theory (B. I. Wiessenschaftsverlag, Mannheim, 1990) 489-502.
  12. M. D. Plummer, Extending matchings in graphs: A survey, Discrete Math. 127 (1994) 277-292, doi: 10.1016/0012-365X(92)00485-A.
  13. Z. Ryjáček, Matching extension in K1,r-free graphs with independent claw centers, to appear in Discrete Math.
  14. W. T. Tutte, The factorization of linear graphs, J. London Math. Soc. 22 (1947) 107-111, doi: 10.1112/jlms/s1-22.2.107.
  15. W. W. Wong and C. K. Wong, Minimum k-Hamiltonian Graphs, J. Graph Theory 8 (1984) 155-165, doi: 10.1002/jgt.3190080118.
Pages:
41-51
Main language of publication
English
Received
1995-11-13
Published
1996
Exact and natural sciences