Let G be a graph, and g and f be integer valued functions defined on V(G) which satisfy g(x)≤f(x) and g(x)≡f(x)(mod 2) for all x∈V(G). Then a spanning subgraph F of G is called a {g,g+2,…,f} -factor if deg_F(x)∈{...Let G be a graph, and g and f be integer valued functions defined on V(G) which satisfy g(x)≤f(x) and g(x)≡f(x)(mod 2) for all x∈V(G). Then a spanning subgraph F of G is called a {g,g+2,…,f} -factor if deg_F(x)∈{g(x),g(x)+2,…,f(x)} for all x∈V(G), when g(x)=1 for all x∈V(G), such a factor is called (1,f) -odd-factor. We give necessary and sufficient conditions for a graph G to have a {g,g+2,…,f} -factor and a (1,f) -odd-factor which contains an arbitrarily given edge of G, from that we derive some interesting results.展开更多
文摘Let G be a graph, and g and f be integer valued functions defined on V(G) which satisfy g(x)≤f(x) and g(x)≡f(x)(mod 2) for all x∈V(G). Then a spanning subgraph F of G is called a {g,g+2,…,f} -factor if deg_F(x)∈{g(x),g(x)+2,…,f(x)} for all x∈V(G), when g(x)=1 for all x∈V(G), such a factor is called (1,f) -odd-factor. We give necessary and sufficient conditions for a graph G to have a {g,g+2,…,f} -factor and a (1,f) -odd-factor which contains an arbitrarily given edge of G, from that we derive some interesting results.
