New isolated toughness condition for fractional $(g,f,n)$-critical graphs
Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 55-65
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $i(G)$ be the number of isolated vertices in a graph $G$. The isolated toughness of $G$ is defined as $I(G)=\infty $ if $G$ is complete, and $I(G)=\operatorname{min}\{|S|/i(G-S) : S\subseteq V(G),\, i(G-S)\ge 2\}$ otherwise. We show that $G$ is a fractional $(g,f,n)$-critical graph if $I(G)\ge (b^{2}+bn-\varDelta )/{a}$, where $a, b$ are positive integers, $1\le a\le b$, $b\ge 2$, and $\varDelta =b-a$. Furthermore, a new isolated toughness condition for fractional $(a,b,n)$-critical graphs is given.
Keywords:
number isolated vertices graph isolated toughness defined infty complete operatorname min g s subseteq g s otherwise fractional critical graph bn vardelta where positive integers vardelta b a furthermore isolated toughness condition fractional critical graphs given
Affiliations des auteurs :
Wei Gao 1 ; Weifan Wang 2
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author = {Wei Gao and Weifan Wang},
title = {New isolated toughness condition for fractional $(g,f,n)$-critical graphs},
journal = {Colloquium Mathematicum},
pages = {55--65},
publisher = {mathdoc},
volume = {147},
number = {1},
year = {2017},
doi = {10.4064/cm6713-8-2016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6713-8-2016/}
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TY - JOUR AU - Wei Gao AU - Weifan Wang TI - New isolated toughness condition for fractional $(g,f,n)$-critical graphs JO - Colloquium Mathematicum PY - 2017 SP - 55 EP - 65 VL - 147 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6713-8-2016/ DO - 10.4064/cm6713-8-2016 LA - en ID - 10_4064_cm6713_8_2016 ER -
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Wei Gao; Weifan Wang. New isolated toughness condition for fractional $(g,f,n)$-critical graphs. Colloquium Mathematicum, Tome 147 (2017) no. 1, pp. 55-65. doi: 10.4064/cm6713-8-2016
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