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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References

SHOWING 1-10 OF 44 REFERENCES
Edge-magic total labelings
TLDR
An edge-magic total labeling on a graph G is a one-to-one map λ from V (G) \ cup E(G) onto the integers 1,2, …, v + e, where wt(xy) = k for any choice of edge xy.
Magic Valuations of Finite Graphs
The purpose of this paper is to investigate for graphs the existence of certain valuations which have some "magic" property. The question about the existence of such valuations arises from the
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 ) .
Circular colorings of weighted graphs
Suppose that G is a finite simple graph and w is a weight function which assigns to each vertex of G a nonnegative real number. Let C be a circle of length t. A t-circular coloring of (G, w) is a
On Additive Bases and Harmonious Graphs
TLDR
This paper first considers several types of additive bases, then a closely related graph labeling problem is studied, and some infinite families of graphs are shown to be harmonious while others (even cycles, most complete or complete...
On a problem of sidon in additive number theory, and on some related problems
To the memory of S. Sidon. Let 0 < a, < a,. .. be an infinite sequence of positive integers. Denote by f(n) the number of solutions of n=a i +a;. About twenty years ago, SIDON 1) raised the question
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn formulae play a prominent role in artificial intelligence and logic programming. In this paper we investigate the problem of optimal compression of propositional Horn production rule knowledge
On a Problem of Sidon in Additive Number Theory and on Some Related Problems Addendum
In a note in this Journal [16 (1941), 212-215], Turan and I proved, among other results, the following : Let a l < a2 < . . . < a, < n be a sequence of positive integers such that the sums aj+a; are
ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS
Let a,<&<... be a sequence of positive integers, and suppose that the suma czi+lzi (where i ,<j) are all different. Such sequences, called B, sequences by Sidont, occur in the theory of Fourier
...
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