# Discrete Mathematics & Theoretical Computer Science

## Volume 6 n° 2 (2004), pp. 401-408

author: | Kayll, P. Mark |
---|---|

title: | Well-spread sequences and edge-labellings with constant Hamilton-weight |

keywords: | Well-spread, weak Sidon, graph labelling, Hamilton cycle |

abstract: | A sequence (a of integers is _{i})well-spread if the sums a, for _{i}+a_{j}i<j, are all different. For a fixed positive integer r,
let W denote the maximum integer _{r}(N)n for which there exists a
well-spread sequence 0≤ a with
_{1}<…<a_{n}≤ Na for all _{i}≡ a_{j}(b mod r)i, j.
We give a new proof that W; our
approach improves a bound of Ruzsa [_{r}(N)<(N/r)^{1/2}+O((N/r)^{1/4})Acta.Arith. 65
(1993), 259--283] by decreasing the
implicit constant, essentially from 4 to √3.
We apply this
result to verify a conjecture of Jones et al. from
[Discuss. Math. Graph Theory 23 (2003),
287--307]. The application concerns the
growth-rate of the maximum label Λ(n) in a `most-efficient'
metric, injective edge-labelling of K with the property that every
Hamilton cycle has the same length; we prove that
_{n}2n.
^{2}-O(n^{3/2})<Λ(n)<2n^{2}+O(n^{61/40})If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

reference: | Kayll, P. Mark (2004),
Well-spread sequences and edge-labellings with constant Hamilton-weight,
Discrete Mathematics and Theoretical Computer Science 6, pp. 401-408 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Di Sep 21 23:33:58 CEST 2004 by gustedt