On constant-weight TSP-tours

@article{Jones2003OnCT,
  title={On constant-weight TSP-tours},
  author={Scott Jones and Peter Mark Kayll and Bojan Mohar and Walter D. Wallis},
  journal={Discuss. Math. Graph Theory},
  year={2003},
  volume={23},
  pages={287-307}
}
Is it possible to label the edges of Kn with distinct integer weights so that every Hamilton cycle has the same total weight? We give a local condition characterizing the labellings that witness this question’s perhaps surprising affirmative answer. More generally, we address the question that arises when “Hamilton cycle” is replaced by “k-factor” for nonnegative integers k. Such edge-labellings are in correspondence with certain vertex-labellings, and the link allows us to determine (up to a… 
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Well-spread sequences and edge-labellings with constant Hamilton-weight
  • P. Kayll
  • Mathematics
    Discret. Math. Theor. Comput. Sci.
  • 2004
TLDR
The application concerns the growth-rate of the maximum label Λ(n) in a `most-efficient' metric, injective edge-labelling of K n with the property that every Hamilton cycle has the same length; it is proved that 2n 2 -O(n 3/2 )<Λ( n)<2n 2 +O( n 61/40 ) .
A note on weak Sidon sequences

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Well-spread sequences and edge-labellings with constant Hamilton-weight
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TLDR
The application concerns the growth-rate of the maximum label Λ(n) in a `most-efficient' metric, injective edge-labelling of K n with the property that every Hamilton cycle has the same length; it is proved that 2n 2 -O(n 3/2 )<Λ( n)<2n 2 +O( n 61/40 ) .
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