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- W2016385416 abstract "Let <TEX>$a$</TEX> and <TEX>$b$</TEX> be two even integers with <TEX>$2{leq}a</TEX><TEX><</TEX><TEX>b$</TEX>, and let k be a nonnegative integer. Let G be a graph of order <TEX>$n$</TEX> with <TEX>$n{geq}frac{(a+b-1)(a+b-2)+bk-2}{b}$</TEX>. A graph G is called an (<TEX>$a,b,k$</TEX>)-critical graph if after deleting any <TEX>$k$</TEX> vertices of G the remaining graph of G has an [<TEX>$a,b$</TEX>]-factor. In this paper, it is proved that G is an (<TEX>$a,b,k$</TEX>)-critical graph if <TEX>$${mid}N_G(X){mid}</TEX><TEX>&</TEX><TEX>gt;frac{(a-1)n+{mid}X{mid}+bk-2}{a+b-1}</TEX><TEX>$$</TEX> for every non-empty independent subset X of V (G), and <TEX>$${delta}(G)</TEX><TEX>></TEX><TEX>frac{(a-1)n+a+b+bk-3}{a+b-1}$$</TEX>. Furthermore, it is shown that the result in this paper is best possible in some sense." @default.
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- W2016385416 date "2013-09-30" @default.
- W2016385416 modified "2023-09-26" @default.
- W2016385416 title "REMARKS ON NEIGHBORHOODS OF INDEPENDENT SETS AND (a, b, k)-CRITICAL GRAPHS" @default.
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- W2016385416 doi "https://doi.org/10.14317/jami.2013.669" @default.
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