The toughness t(G) of graph G is formalized as the minimum ratio of |S| and ?(G - S) over all vertex subsets S subject to ?(G - S) > 1. As the unique variant parameter of toughness, ?(G) is formulated as the minimum ratio of |S| and ?(G - S) - 1 traversing all the vertex subset S restricted to ?(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 ?(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 ?(G) > k for k ? 3 and if ?(G)>3/2 for k = 2. The sharpness of the given bounds is explained by counterexamples.

Rights

URN

URN:NBN:SI:doc-D3NYGZDH

COBISSID

288347907

DOI

10.26493/1855-3974.3161.63b

Added

27.10.2026

Metadata

Citation

APA:

Gao, Wei, Wang, Weifan, Chen, Yaojun (2026). Tight toughness variant condition for fractional k-factors. Ars mathematica contemporanea, volume 26, issue 1, article p1.04, str. 1-23. URN:NBN:SI:doc-D3NYGZDH from http://www.dlib.si

MLA:

Gao, Wei, Wang, Weifan, Chen, Yaojun. "Tight toughness variant condition for fractional k-factors." Ars mathematica contemporanea volume 26. issue 1. article p1.04 (2026) str. 1-23.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-D3NYGZDH>

Ars mathematica contemporanea
2008-
(Assembly record)