S4 separation and p-partition in all-path and detour convexities

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dc.contributor.authorHaponenko, Vladyslaven_US
dc.date.accessioned2026-06-01T13:38:31Z
dc.date.available2026-06-01T13:38:31Z
dc.date.issued2026
dc.description.abstractIn this work, we consider problems of S4 and p-convex partition separations with respect to the all-path and the detour convexities. We give characterizations of p-all-path convex and p-detour convex graphs. With respect to all-path convexity S2, S3, and S4 separable graphs are characterized. Also, we present necessary and sufficient conditions for two sets to be S4 separable, for both convexities. Moreover, we prove that in all-path convexity the time complexity of those problems is linear, and it is NP-hard for detour convexity. Finally, we give an algorithm for determining whether two sets in graph are S4 separable with respect to all-path convexity.en_US
dc.identifier.citationHaponenko V. S4 separation and p-partition in all-path and detour convexities / V. Haponenko // TWMS Journal of Applied and Engineering Mathematics. - 2026. - Vol. 16, Issue 4. - P. 443-456. - https://jaem.isikun.edu.tr/web/index.php/current/142-vol16no4/1579-s4-separation-and-p-partition-in-all-path-and-detour-convexitiesen_US
dc.identifier.issn2587-1013
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/39871
dc.language.isoen_USen_US
dc.relation.sourceTWMS Journal of Applied and Engineering Mathematicsen_US
dc.statusfirst publisheden_US
dc.subjectall-path convexityen_US
dc.subjectgraph convexityen_US
dc.subjectdetour convexityen_US
dc.subjectconvex separationen_US
dc.subjectp-partitionen_US
dc.subjectarticleen_US
dc.titleS4 separation and p-partition in all-path and detour convexitiesen_US
dc.typeArticleen_US
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