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Note on Semi-Linkage with Almost Prescribed Lengths in Large Graphs

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Abstract

We prove a sharp connectivity and degree sum condition for the existence of a subdivision of a multigraph in which some of the vertices are specified and the distance between each pair of vertices in the subdivision is prescribed (within one). Our proof makes use of the powerful Regularity Lemma in an easy way that highlights the extreme versatility of the lemma.

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References

  1. Chartrand, G., Lesniak, L., Zhang, P.: Graphs & Digraphs, 5th edn. CRC Press, Boca Raton (2011)

    MATH  Google Scholar 

  2. Coll, V., Halperin, A., Magnant, C., Salehi Nowbandegani, P.: Enomoto and Ota’s conjecture holds for large graphs (2014). (Submitted)

  3. Diestel, R.: Graph theory. In: Graduate Texts in Mathematics, 4th edn, vol 173. Springer, Heidelberg (2010)

  4. Enomoto, H., Ota, K.: Partitions of a graph into paths with prescribed endvertices and lengths. J. Graph Theory 34(2), 163–169 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Faudree, R.J., Gould, R.J.: Precise location of vertices on Hamiltonian cycles. Discret. Math. 313(23), 2772–2777 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Faudree, R.J., Gould, R.J., Jacobson, M.S., Magnant, C.: Distributing vertices on Hamiltonian cycles. J. Graph Theory 69(1), 28–45 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Faudree, R.J., Lehel, J., Yoshimoto, K.: Note on locating pairs of vertices on Hamiltonian cycles. Graphs Comb. 30(4), 887–894 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hall, M., Magnant, C., Wang, H.: Note on Enomoto and Ota’sconjecture for short paths in large graphs. Graphs Comb. 30(6), 1463–1467 (2014)

  9. Kaneko, A., Yoshimoto, K.: On a Hamiltonian cycle in which specified vertices are uniformly distributed. J. Comb. Theory Ser. B 81(1), 100–109 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  10. Komlós, J., Sárközy, G.N., Szemerédi, E.: Blow-up lemma. Combinatorica 17(1), 109–123 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kühn, D., Osthus, D., Treglown, A.: An Ore-type theorem for perfect packings in graphs. SIAM J. Discret. Math. 23(3), 1335–1355 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Magnant, C., Martin, D.M.: An asymptotic version of a conjecture by Enomoto and Ota. J. Graph Theory 64(1), 37–51 (2010)

    MathSciNet  MATH  Google Scholar 

  13. Magnant, C., Salehi Nowbandegani, P.: Note on lengths of cycles containing a specified edge (2015). (Submitted)

  14. Ore, O.: Note on Hamilton circuits. Am. Math. Mon. 67, 55 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  15. Szemerédi, E.: Regular partitions of graphs. In: Problèmes Combinatoires et Théorie des Graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976), volume 260 of Colloq. Internat. CNRS, pp. 399–401. CNRS, Paris (1978)

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Acknowledgments

The authors would like to thank the referees very much for their helpful comments and suggestions that greatly improved this work.

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Authors and Affiliations

  1. Georgia Southern University, Statesboro, GA, USA

    Emily Chizmar & Colton Magnant

  2. Mosow Institute of Physics and Technology, Moscow, Russia

    Pouria Salehi Nowbandegani

Authors
  1. Emily Chizmar
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  2. Colton Magnant
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  3. Pouria Salehi Nowbandegani
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Correspondence to Colton Magnant.

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Chizmar, E., Magnant, C. & Salehi Nowbandegani, P. Note on Semi-Linkage with Almost Prescribed Lengths in Large Graphs. Graphs and Combinatorics 32, 881–886 (2016). https://doi.org/10.1007/s00373-015-1631-5

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  • DOI: https://doi.org/10.1007/s00373-015-1631-5

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