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- W3196717178 abstract "<abstract><p>Let $ G $ be a graph. For a set $ mathcal{H} $ of connected graphs, an $ mathcal{H} $-factor of a graph $ G $ is a spanning subgraph $ H $ of $ G $ such that every component of $ H $ is isomorphic to a member of $ mathcal{H} $. A graph $ G $ is called an $ (mathcal{H}, m) $-factor deleted graph if for every $ E'subseteq E(G) $ with $ |E'| = m $, $ G-E' $ admits an $ mathcal{H} $-factor. A graph $ G $ is called an $ (mathcal{H}, n) $-factor critical graph if for every $ Nsubseteq V(G) $ with $ |N| = n $, $ G-N $ admits an $ mathcal{H} $-factor. Let $ m $, $ n $ and $ k $ be three nonnegative integers with $ kgeq2 $, and write $ mathcal{F} = {P_2, C_3, P_5, mathcal{T}(3)} $ and $ mathcal{H} = {K_{1, 1}, K_{1, 2}, cdots, K_{1, k}, mathcal{T}(2k+1)} $, where $ mathcal{T}(3) $ and $ mathcal{T}(2k+1) $ are two special families of trees. In this article, we verify that (i) a $ (2m+1) $-connected graph $ G $ is an $ (mathcal{F}, m) $-factor deleted graph if its binding number $ bind(G)geqfrac{4m+2}{2m+3} $; (ii) an $ (n+2) $-connected graph $ G $ is an $ (mathcal{F}, n) $-factor critical graph if its binding number $ bind(G)geqfrac{2+n}{3} $; (iii) a $ (2m+1) $-connected graph $ G $ is an $ (mathcal{H}, m) $-factor deleted graph if its binding number $ bind(G)geqfrac{2}{2k-1} $; (iv) an $ (n+2) $-connected graph $ G $ is an $ (mathcal{H}, n) $-factor critical graph if its binding number $ bind(G)geqfrac{2+n}{2k+1} $.</p></abstract>" @default.
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- W3196717178 date "2021-01-01" @default.
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- W3196717178 title "Component factors and binding number conditions in graphs" @default.
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