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- W1523843921 abstract "Let a,b,k be nonnegative integers with 2⩽a<b and b⩾a(k+1). An [a,b]-factor of a graph G is defined as a spanning subgraph F of G such that a⩽dF(x)⩽b for each x∈V(G). A graph G is called an (a,b,k)-critical graph if after deleting any k vertices of G the remaining graph of G has an [a,b]-factor. This toughness of a graph G, denoted by t(G), is defined as t(G)=min{|S|ω(G−S):S⊆V(G),ω(G−S)⩾2} if G is not complete; otherwise, t(G)=+∞. In this paper, it is proved that a graph G is an (a,b,k)-critical graph if G satisfies δ(G)⩾a+k and t(G)⩾a−1+(a−1)(k+1)b. Furthermore, it is shown that the result in this paper is best possible in some sense." @default.
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- W1523843921 date "2011-04-01" @default.
- W1523843921 modified "2023-09-23" @default.
- W1523843921 title "Toughness and -critical graphs" @default.
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- W1523843921 doi "https://doi.org/10.1016/j.ipl.2011.01.012" @default.
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