Geodesic
A proof of the two-path conjecture
The electronic journal of combinatorics, Tome 9 (2002)
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Let $G$ be a connected graph that is the edge-disjoint union of two paths of length $n$, where $n\ge2$. Using a result of Thomason on decompositions of 4-regular graphs into pairs of Hamiltonian cycles, we prove that $G$ has a third path of length $n$.
DOI : 10.37236/1665
Classification : 05C38, 05C70
Mots-clés : connected graph, path 
@article{10_37236_1665,
     author = {Herbert Fleischner and Robert R. Molina and Ken W. Smith and Douglas B. West},
     title = {A proof of the two-path conjecture},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1665},
     zbl = {1003.05064},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1665/}
}
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Herbert Fleischner; Robert R. Molina; Ken W. Smith; Douglas B. West. A proof of the two-path conjecture. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1665

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