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arXiv · 1805.04378

Revisiting the Hamiltonian Theme in the Square of a Block: The General Case

Herbert Fleischner·Gek L. Chia
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Abstract

This is the second part of joint research in which we show that every $2$-connected graph $G$ has the ${\cal F}_4$ property. That is, given distinct $x_i\in V(G)$, $1\leq i\leq 4$, there is an $x_1x_2$-hamiltonian path in $G^2$ containing different edges $x_3y_3, x_4y_4\in E(G)$ for some $y_3,y_4\in V(G)$. However, it was shown already in \cite[Theorem 2]{cf1:refer} that 2-connected DT-graphs have the ${\cal F}_4$ property; based on this result we generalize it to arbitrary $2$-connected graphs. We also show that these results are best possible.

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Herbert Fleischner, Gek L. Chia. 2018-05-11. Revisiting the Hamiltonian Theme in the Square of a Block: The General Case. https://arxiv.org/abs/1805.04378

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