Haponenko, VladyslavKozerenko, Sergiy2024-05-212024-05-212024Haponenko V. All-path convexity: two characterizations, general position number, and one algorithm / Vladyslav Haponenko, Sergiy Kozerenko // Discrete Mathematics Letters. - 2024. - Vol. 13. - P. 58-65. - https://doi.org/10.47443/dml.2024.0142664-2557https://doi.org/10.47443/dml.2024.014https://ekmair.ukma.edu.ua/handle/123456789/29549We present two characterizations for the all-path convex sets in graphs. Using the first criterion, we obtain a new characterization of connected block graphs and compute the general position number in a graph with respect to the all-path convexity. The second criterion allows us to provide a new algorithm for testing a set on all-path convexity.enall-path convexitygraph convexityinterval spaceblock graphgated setgeneral position numberarticleArticle