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• W4295981808 abstract "Isolated toughness of graph G is formulated by minimizing the ratio |S|/i(G−S) over all S⊆V(G) with i(G−S)≥2, where i(G−S) is the number of isolated vertices after removing vertex subset S from G. The previous works reveal that there exist explicit correlations between isolated toughness and fractional critical graphs (a.k.a. the graph admits a fractional factor after deleting given number of vertices). However, among the existing isolated toughness bounds, the term with respect to n (the number of removed vertices) is always at least n. In this paper, the exactly sharp isolated toughness bound for fractional (k,n)-critical graph is determined which reveals that the coefficient of term with regard to n can be reduced to 1/2. It is well acknowledged that some tight toughness related bounds can reach to the extreme value, while others cannot. We give an explanation why these tight bounds in various settings possess such pattern differences." @default.
• W4295981808 created "2022-09-16" @default.
• W4295981808 creator A5053672565 @default.
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• W4295981808 date "2022-12-01" @default.
• W4295981808 modified "2023-10-14" @default.
• W4295981808 title "Tight isolated toughness bound for fractional <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline id=d1e71 altimg=si14.svg><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-critical graphs" @default.
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• W4295981808 doi "https://doi.org/10.1016/j.dam.2022.08.028" @default.
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