Spanning trails with variations of Chvátal–Erdős conditions

Let α(G), α′(G), κ(G) and κ′(G) denote the independence number, the matching number, connectivity and edge connectivity of a graph G, respectively. We determine the finite graph families F1 and F2 such that each of the following holds.(i) If a connected graph G satisfies κ′(G)≥α(G)−1, then G has a spanning closed trail if and only if G is not contractible to a member of F1.(ii) If κ′(G)≥max{2,α(G)−3}, then G has a spanning trail. This result is best possible.(iii) If a connected graph G satisfies κ′(G)≥3 and α′(G)≤7, then G has a spanning closed trail if and only if G is not contractible to a member of F2

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum