Königsberg Sightseeing: Eulerian Walks in Temporal Graphs

An Eulerian walk (or trail) is a (resp. that visits every edge of graph G at least exactly) once. This notion was first discussed by Leonhard Euler while solving the famous Seven Bridges Königsberg problem in 1736. But what if had to take bus? In temporal $$(G,\lambda )$$ , with $$\lambda : E(G)\rightarrow 2^{[\tau ]}$$ an $$e\in E(G)$$ available only times specified (e)\subseteq [\tau ]$$ same way connections public transportation network city or sightseeing tours are scheduled times. this scenario, even though several translations trails and walks possible terms, very particular variation has been exploited literature, specifically for infinite dynamic networks (Orlin, 1984). paper, we deal walks, local trails, respectively referring traversal no constraints, constrained not repeating single timestamp, never throughout entire traversal. We show that, edges always available, then deciding whether trail polynomial, it $$\textsf {NP}$$ -complete lifetime 2. contrast, general case, any these problems -complete, under strict hypotheses.