Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v...Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v∈V(G).In this paper,we prove that every graph G with n≥2(b+1)(a+b) vertices has all(a,b)-parity factors if δ(G)≥(b^(2)-b)/a,and for any two nonadjacent vertices u,v ∈V(G),max{d_(G)(u),d_(G)(v)}≥bn/a+b.Moreover,we show that this result is best possible in some sense.展开更多
基金supported by the National Natural Science Foundation of China (No.12271425 and No.11871391)。
文摘Let a and b be positive integers such that a≤b and a≡b(mod 2).We say that G has all(a,b)-parity factors if G has an h-factor for every function h:V(G)→{a,a+2,…,b-2,b} with b|V(G)| even and h(v)≡b(mod 2) for all v∈V(G).In this paper,we prove that every graph G with n≥2(b+1)(a+b) vertices has all(a,b)-parity factors if δ(G)≥(b^(2)-b)/a,and for any two nonadjacent vertices u,v ∈V(G),max{d_(G)(u),d_(G)(v)}≥bn/a+b.Moreover,we show that this result is best possible in some sense.
