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Fullerene graphs have exponentially many perfect matchings

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Abstract

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.

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References

  1. Appel K., Haken W.: Every planar map is four colorable. Part I.. Discharging. Illinois J. Math. 21, 429–490 (1977)

    Google Scholar 

  2. Appel K., Haken W., Koch J.: Every planar map is four colorable. Part II. Reducibility. Illinois J. Math. 21, 491–567 (1977)

    Google Scholar 

  3. M. Chudnovsky, P. Seymour, Perfect matchings in planar cubic graphs. Submitted for publication (2008)

  4. Došlić T.: On lower bounds of number of perfect matchings in fullerene graphs. J. Math. Chem. 24, 359–364 (1998)

    Article  Google Scholar 

  5. Došlić T.: On some structural properties of fullerene graphs. J. Math. Chem. 31, 187–195 (2002)

    Article  Google Scholar 

  6. Došlić T.: Cyclical edge-connectivity of fullerene graphs and (k,6)-cages. J. Math. Chem 33, 103–112 (2003)

    Article  Google Scholar 

  7. Došlić T.: Fullerene graphs with exponentially many perfect matchings. J. Math. Chem. 42(2), 183–192 (2007)

    Google Scholar 

  8. Došlić T.: Leapfrog fullerenes have many perfect matchings. J. Math. Chem. 44(1), 1–4 (2008)

    Article  Google Scholar 

  9. Erdős P., Rubin A.L., Taylor H.: Choosability in graphs. Congr. Numer. 26, 122–157 (1980)

    Google Scholar 

  10. Kardoš F., Škrekovski R.: Cyclic edge-cuts in fullerene graphs. J. Math. Chem. 44(1), 121–132 (2008)

    Article  Google Scholar 

  11. Klein D.J., Liu X.: Theorems for carbon cages. J. Math. Chem 11, 199–205 (1992)

    Article  CAS  Google Scholar 

  12. Kroto H.W., Heath J.R., O’Brien S.C., Curl R.F., Smalley R.E.: C60 Buckminsterfullerene. Nature 318, 162–163 (1985)

    Article  CAS  Google Scholar 

  13. K. Kutnar, D. Marušič, On cyclic edge-connectivity of fullerenes. Preprint, arXiv:math-CO/0702511

  14. Robertson N., Sanders D.P., Seymour P.D., Thomas R.: The four colour theorem. J. Combin. Theory Ser. B 70, 2–44 (1997)

    Article  Google Scholar 

  15. Vizing V.G.: Colouring the vertices of a graph in prescribed colours (in Russian). Diskret. Anal. 29, 3–10 (1976)

    Google Scholar 

  16. Zhang H., Zhang F.: New lower bound on the number of perfect matchings in fullerene graphs. J. Math. Chem. 30, 343–347 (2001)

    CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Science, University of Pavol Jozef Šafárik, Jesenná 5, 041 54, Košice, Slovakia

    František Kardoš & Jozef Miškuf

  2. Institute for Theoretical Computer Science (ITI), Faculty of Mathematics and Physics, Charles University, Malostranské Náměstí 25, 118 00, Prague, Czech Republic

    Daniel Král’

  3. Department of Applied Mathematics (KAM) and DIMATIA, Faculty of Mathematics and Physics, Charles University, Malostranské Náměstí 25, 118 00, Prague, Czech Republic

    Jean-Sébastien Sereni

Authors
  1. František Kardoš
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  2. Daniel Král’
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  3. Jozef Miškuf
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  4. Jean-Sébastien Sereni
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Correspondence to František Kardoš.

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Kardoš, F., Král’, D., Miškuf, J. et al. Fullerene graphs have exponentially many perfect matchings. J Math Chem 46, 443–447 (2009). https://doi.org/10.1007/s10910-008-9471-7

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  • DOI: https://doi.org/10.1007/s10910-008-9471-7

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