Geodesic
On Path-Pairability in the Cartesian Product of Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 743-758

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We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product. We present path-pairable graph families that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.
Keywords: path-pairable graphs, Cartesian product of graphs 
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     author = {M\'esz\'aros, G\'abor},
     title = {On {Path-Pairability} in the {Cartesian} {Product} of {Graphs}},
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Mészáros, Gábor. On Path-Pairability in the Cartesian Product of Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 3, pp. 743-758. http://geodesic.mathdoc.fr/item/DMGT_2016_36_3_a16/