Geodesic
Absolute differences along Hamiltonian paths
Francesco Monopoli1
1Università degli Studi di Milano
The electronic journal of combinatorics, Tome 22 (2015) no. 3

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Zbl arXiv
We prove that if the vertices of a complete graph are labeled with the elements of an arithmetic progression, then for any given vertex there is a Hamiltonian path starting at this vertex such that the absolute values of the differences of consecutive vertices along the path are pairwise distinct. In another extreme case where the label set has small additive energy, we show that the graph actually possesses a Hamiltonian cycle with the property just mentioned. These results partially solve a conjecture by Z.-W. Sun.
DOI : 10.37236/5159
Classification : 05C38
Mots-clés : Hamiltonian paths

Francesco Monopoli  1

1 Università degli Studi di Milano 
Francesco Monopoli. Absolute differences along Hamiltonian paths. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5159
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     author = {Francesco Monopoli},
     title = {Absolute differences along {Hamiltonian} paths},
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     year = {2015},
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     number = {3},
     doi = {10.37236/5159},
     zbl = {1327.05176},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5159/}
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