no. 5
Isolated toughness variant and fractional k -factor
RAIRO. Operations Research, Tome 56 (2022) no. 5, pp. 3675-3688

Isolated toughness is a crucial parameter considered in network security which characterizes the vulnerability of the network from the perspective of graph topology. I’(G) is the unique variant of isolated toughness which was introduced in 2001. This work investigates the correlation of I’(G) and the existence of fractional factor. It is proved that a graph G with δ(G) ≥ k admits fraction k-factor if I’(G) > 2k − 1, where k ≥ 2 is an integer. A counterexample is presented to show the sharpness of I’(G) bound.

DOI : 10.1051/ro/2022177
Classification : 05C70
Keywords: Graph, isolated toughness, fractional $$-factor 
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     title = {Isolated toughness variant and fractional $k$-factor},
     journal = {RAIRO. Operations Research},
     pages = {3675--3688},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {5},
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     mrnumber = {4502919},
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     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2022177/}
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He, Zhengyue; Liang, Li; Gao, Wei. Isolated toughness variant and fractional $k$-factor. RAIRO. Operations Research, Tome 56 (2022) no. 5, pp. 3675-3688. doi: 10.1051/ro/2022177

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