Abstract
A graph is called $$2K_2$$ -free if it does not contain two independent edges as an induced subgraph. Gao and Pasechnik conjectured that every $$\frac{3}{2}$$ -tough $$2K_2$$ -free graph with at least three vertices has a spanning trail with maximum degree at most 4. In this paper, we confirm this conjecture. We also provide examples for all $$t < \frac{5}{4}$$ of t-tough graphs that do not have a spanning trail with maximum degree at most 4.
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