Geodesic
Hamiltonian cycles in the square of a graph
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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We show that under certain conditions the square of the graph obtained by identifying a vertex in two graphs with hamiltonian square is also hamiltonian. Using this result, we prove necessary and sufficient conditions for hamiltonicity of the square of a connected graph such that every vertex of degree at least three in a block graph corresponds to a cut vertex and any two these vertices are at distance at least four.
DOI : 10.37236/690
Classification : 05C45, 05C38, 05C40
Mots-clés : Hamiltonian cycle, connection of graphs, block graph, square, star 
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     author = {Jan Ekstein},
     title = {Hamiltonian cycles in the square of a graph},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/690},
     zbl = {1229.05196},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/690/}
}
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Jan Ekstein. Hamiltonian cycles in the square of a graph. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/690

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