Geodesic
On the Buratti-Horak-Rosa conjecture about Hamiltonian paths in complete graphs
Anita Pasotti1 ; Marco Antonio Pellegrini2
1Università degli Studi di Brescia
2Università Cattolica del Sacro Cuore
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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In this paper we investigate a problem proposed by Marco Buratti, Peter Horak and Alex Rosa (denoted by BHR-problem) concerning Hamiltonian paths in the complete graph with prescribed edge-lengths. In particular we solve BHR$(\{1^a, 2^b, t^c\})$ for any even integer $t \geq 4$, provided that $a+b \geq t-1$. Furthermore, for $t=4, 6, 8$ we present a complete solution of BHR$(\{ 1^a,2^b,t^c \})$ for any positive integer $a,b,c$.
DOI : 10.37236/3879
Classification : 05C38, 05C45
Mots-clés : Hamiltonian path, complete graph, edge-length

Anita Pasotti  1   ; Marco Antonio Pellegrini  2

1 Università degli Studi di Brescia
2 Università Cattolica del Sacro Cuore 
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     title = {On the {Buratti-Horak-Rosa} conjecture about {Hamiltonian} paths in complete graphs},
     journal = {The electronic journal of combinatorics},
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Anita Pasotti; Marco Antonio Pellegrini. On the Buratti-Horak-Rosa conjecture about Hamiltonian paths in complete graphs. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3879

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