| Title: | Tight toughness variant condition for fractional k-factors |
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| Authors: | ID Gao, Wei (Author)
ID Wang, Weifan (Author)
ID Chen, Yaojun (Author) |
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| Files: |  AMC_Gao,_Wang,_Chen_2026.pdf (1,11 MB)
MD5: 1F614C9B844CD0531E8F714A781C4987
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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. |
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| Keywords: | graph, toughness, toughness variant, fractional k-factor |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 17.11.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 23 str. |
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| Numbering: | Vol. 26, no. 1, [article no.] P1.04 |
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| PID: | 20.500.12556/RUP-22288  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3161.63b |
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| Publication date in RUP: | 21.12.2025 |
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| Views: | 186 |
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| Downloads: | 0 |
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