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Note on Enomoto and Ota’s Conjecture for Short Paths in Large Graphs

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Abstract

With sufficient minimum degree sum, Enomoto and Ota conjectured that for any selected set of vertices, there exists a spanning collection of disjoint paths, each starting at one of the selected vertices and each having a prescribed length. Using the Regularity Lemma, we prove that this claim holds without the spanning assumption if the vertex set of the host graph is sufficiently large.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA

    Martin Hall, Colton Magnant & Hua Wang

Authors
  1. Martin Hall
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  2. Colton Magnant
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  3. Hua Wang
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Corresponding author

Correspondence to Colton Magnant.

Additional information

C. Magnant was supported by Georgia Southern Faculty Research Committee Research Competition Award. H. Wang’s work was partially supported by a grant from the Simons Foundation (#245307).

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Hall, M., Magnant, C. & Wang, H. Note on Enomoto and Ota’s Conjecture for Short Paths in Large Graphs. Graphs and Combinatorics 30, 1463–1467 (2014). https://doi.org/10.1007/s00373-013-1351-7

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  • DOI: https://doi.org/10.1007/s00373-013-1351-7

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