20.500.12556/RUP-22288 Tight toughness variant condition for fractional k-factors Strogi pogoj variante trdnosti delnih k-faktorjev The toughness t(G) of graph G is formalized as the minimum ratio of |S| and ω(G − S) over all vertex subsets S subject to ω(G − S) > 1. As the unique variant parameter of toughness, τ(G) is formulated as the minimum ratio of |S| and ω(G − S) − 1 traversing all the vertex subset S restricted to ω(G − S) ≥ 2. The extant contributions reveal that there is a substantial correlation between toughness and fractional factors. However, there is still a paucity of solid studies on toughness variants τ(G). This work provides several theoretical underpinnings for the tight toughness variant bound for a graph G which admits a fractional k-factor. To be specific, a graph G has a fractional k-factor if τ(G) > k for k ≥ 3 and if τ(G)>3/2 for k = 2. The sharpness of the given bounds is explained by counterexamples. graph toughness toughness variant fractional k-factor graf trdnost varianta trdnosti delni k-faktor true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-12-21 22:32:44 2025-12-21 22:32:44 2026-01-05 11:59:31 0000-00-00 00:00:00 2026 0 0 23 str. no. 1, [article no.] P1.04 Vol. 26 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-11-17 51 1855-3974 10.26493/1855-3974.3161.63b AMC_Gao,_Wang,_Chen_2026.pdf AMC_Gao,_Wang,_Chen_2026.pdf 1 1F614C9B844CD0531E8F714A781C4987 0614740f42b0e0ae78f641366c9d98797ecc0262aad8af6bdb338f72e6dc4ee4 7f6c0f4b-deb5-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32369 Založba Univerze na Primorskem 0 0 0