Abstract
In this paper info cyclic connectivity is studied in relation to certain matching properties in regular graphs. Results giving sufficient conditions in terms of cyclic connectivity for regular graphs to be factor-critical, to be 3-factor-critical, to have the restricted matching properties E(m, n) and to have defect-d matchings are obtained.
Similar content being viewed by others
References
Aldred R.E.L., Holton D.A., Porteous M.I., Plummer M.D.: Two results on matching extensions with prescribed and proscribed edge sets. Discret. Math. 206, 35–43 (1999)
Aldred R.E.L., Plummer M.D.: Edge proximity and matching extension in planar triangulations. Australas. J. Combin. 29, 215–224 (2004)
Aldred R.E.L., Plummer M.D.: On matching extensions with prescribed and proscribed edge sets II. Discret. Math. 197(198), 29–40 (1999)
Aldred R.E.L., Plummer M.D.: On restricted matching extension in planar graphs. Discret. Math. 231, 73–79 (2001)
Aldred R.E.L., Plummer M.D.: Restricted matching in graphs of small genus. Discret. Math. 308, 5907–5921
Birkhoff G.D.: The reducibility of maps. Am. J. Math. 35, 115–128 (1913)
Fischer I., Little C.H.C.: A characterization of Pfaffian near bipartite graphs. J. Combin. Theory Ser. B 82, 175–222 (2001)
Holton, D., Plummer, M.D.: 2 V-extendability in 3V-polytopes, Combinatorics (Eger, 1987). Colloq. Math. Soc. Jnos Bolyai, 52, 281–300, North-Holland, Amsterdam (1988)
Little C.H.C., Rendl F., Fischer I.: Towards a characterization of Pfaffian near bipartite graphs. Discret. Math. 244, 279–297 (2002)
Liu G.Z., Yu Q.L.: Generalization of matching extensions in graphs. Discret. Math. 231, 311–320 (2001)
Lou D.J., Holton D.A.: Lower bound of cyclic edge connectivity for n-extendability of regular graphs. Discret. Math. 112, 139–150 (1993)
Lou D., Wang W.: An efficient algorithm for cyclic edge connectivity of regular graphs. Ars Combin. 77, 311–318 (2005)
Lovász, L., Plummer, M.D.: Matching theory, North-Holland mathematics studies, vol. 121. Ann. Discret. Math., 29. North-Holland Publishing Co., Amsterdam, Akadémiai Kiadó, Budapest (1986)
McGregor-Macdonald, A.: The E(m, n) property. M.S. thesis, University of Otago, Dunedin, New Zealand (2000)
Miranda A., Lucchesi C.: Recognizing near-bipartite Pfaffian graphs in polynomial time. Discret. Appl. Math. 158, 1275–1278 (2010)
Naddef D., Pulleyblank W.R.: Matchings in regular graphs. Discret. Math. 34, 283–291 (1981)
Péroche B.: On several sorts of connectivity. Discret. Math. 46, 267–277 (1983)
Plesní k J.: Connectivity of regular graphs and the existence of 1-factors. Mat. Časopis Sloven. Akad. Vied. 22, 310–318 (1972)
Plesní k J.: Remark on matchings in regular graphs. Acta Fac. Rerum Natur. Univ. Comenian. Math. 34, 63–67 (1979)
Plummer M.D.: Extending matchings in graphs: a survey. Discret. Math. 127, 277–292 (1994)
Plummer M.D.: Extending matchings in graphs: an update. Congr. Numer. 116, 3–32 (1996)
Plummer, M.D.: Matching extension in regular graphs, Graph theory, combinatorics, algorithms, and applications (San Francisco, CA, 1989), pp. 416–436. SIAM, Philadelphia (1991)
Plummer M.D.: On n-extendable graphs. Discret. Math. 31, 201–210 (1980)
Porteous M.I., Aldred R.E.L.: Matching extensions with prescribed and forbidden edges. Australas. J. Combin. 13, 163–174 (1996)
Wang H.: On independent cycles in a bipartite graph. Graphs Combin. 17, 177–183 (2001)
West, D.: Introduction to graph theory, 2nd edn. Prentice-Hall Inc., Upper Saddle River (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
This work supported partially by the Natural Sciences and Engineering Research Council of Canada.
Rights and permissions
About this article
Cite this article
Plummer, M.D., Wang, T. & Yu, Q. A Note on Cyclic Connectivity and Matching Properties of Regular Graphs. Graphs and Combinatorics 30, 1003–1011 (2014). https://doi.org/10.1007/s00373-013-1310-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00373-013-1310-3