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$k$-pairable graph; pair length; Cartesian product; $G$-layer; tree

References:

[1] Z. Chen: **On $k$-pairable graphs**. Discrete Math. 287 (2004), 11–15. DOI 10.1016/j.disc.2004.04.012 | MR 2094052 | Zbl 1050.05026

[2] N. Graham, R. C. Entringer, L. A. Székely: **New tricks for old trees: maps and the pigeonhole principle**. Amer. Math. Monthly 101 (1994), 664–667. DOI 10.2307/2974696 | MR 1289277

[3] W. Imrich, S. Klavžar: **Product Graphs: Structure and Recognition. Wiley-Interscience Series in Discrete Mathematics and Optimization**. Wiley, Chichester, 2000. MR 1788124