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≥4, provided that a+b≥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.
Pasotti, A., Pellegrini, M. A., On the Buratti-Horak-Rosa Conjecture about Hamiltonian Paths in Complete Graphs, <<ELECTRONIC JOURNAL OF COMBINATORICS>>, 2014; (2): N/A-N/A [http://hdl.handle.net/10807/58213]
On the Buratti-Horak-Rosa Conjecture about Hamiltonian Paths in Complete Graphs
Pellegrini, Marco Antonio
2014
Abstract
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≥4, provided that a+b≥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.
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