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We say that a simple graph G is fractional independent-set-deletable k-factor-critical, shortly, fractional ID-k-factor-critical, if G − I has a fractional k-factor for every independent set I of G. Some sufficient conditions for a graph to be fractional ID-k-factor-critical are studied in this paper. Furthermore, we show that the result is best possible in(More)
Let S be a finite set of positive integers. A mixed hypergraph H is a one-realization of S if its feasible set is S and each entry of its chromatic spectrum is either 0 or 1. The smallest one-realization of a given set II, Discrete Math. 312 (2012) 2946–2951], we determined the minimum number of vertices of a 3-uniform bi-hypergraph which is a(More)
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