An independent set degree condition for fractional critical deleted graphs
Let i≥2">i≥2i≥2, Δ≥0">Δ≥0Δ≥0, 1≤a≤b−Δ">1≤a≤b−Δ1≤a≤b−Δ, n>(a+b)(ib+2m−2)a+n′">n>(a+b)(ib+2m−2)a+n′n>(a+b)(ib+2m−2)a+n′ and δ(G)≥b2a+n′+2m">δ(G)≥b2a+n′+2mδ(G)≥b2a+n′+2m, and let g,f">g,fg,f be two integer-valued functions defined on V(G)">V(G)V(G) such that a≤g(x)≤f(x)−Δ≤b−Δ">a≤g(x)≤f(x)−Δ≤b−Δa≤g(x)≤f(x)−Δ≤b−Δ for each x∈V(G)">x∈V(G)x∈V(G). In this article, it is determined that G">GG is a fractional (g,f,n′,m)">(g,f,n′,m)(g,f,n′,m)-critical deleted graph if max{d1,d2,···,di}≥b(n+n′)a+b">max{d1,d2,⋅⋅⋅,di}≥b(n+n′)a+bmax{d1,d2,···,di}≥b(n+n′)a+b for any independent subset {x1,x2,...,xi}⊆V(G)">{x1,x2,...,xi}⊆V(G){x1,x2,...,xi}⊆V(G). The result is tight on independent set degree condition. إقراء المزيد