AbstractLet a1,a2,…,an and b1,b2,…,bn be integers with 0⩽ai⩽bi for i=1,2,…,n. The purpose of this note is to give a good characterization for the existence of a simple graph G with vertices v1,v2,…,vn such that ai⩽dG(vi)⩽bi for i=1,2,…,n. This solves a research problem posed by Niessen and generalizes an Erdős–Gallai theorem
AbstractLet 1≤a<b be integers and G a graph of order n sufficiently large for a and b. Then G has an...
AbstractFor a finite simple graph G, we denote the set of degrees of its vertices, known as its degr...
AbstractWe prove the following theorem: Let G be a graph with vertex-set V and ƒ, g be two integer-v...
AbstractLet a1,a2,…,an and b1,b2,…,bn be integers with 0⩽ai⩽bi for i=1,2,…,n. The purpose of this no...
Let a1,a2,...,an, and b1,b2,...,bn be integers with 0 ≤ ai ≤ bi for i = 1,2,...,n. The purpose of th...
Graph TheoryLet (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) be two sequences of nonnegativ...
AbstractWe show that the Erdős–Gallai condition characterizing graphical degree sequences of length ...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractLet t(⩾3), a and b be integers with 0⩽a<b. A graph is called K1,t-free if it contains no K1,...
AbstractLet d1, d2, …,dn be the degree sequence of a simple graph and suppose p is a positive intege...
summary:The minimum orders of degree-continuous graphs with prescribed degree sets were investigated...
AbstractLet G be a graph on X, and let f(x), g(x) be positive integers; several authors have given c...
AbstractLet G be a graph of order n, and let a and b be integers such that 1⩽a<b. Then we prove that...
AbstractFor any finite sequence of groups G0⊆G1⊆⋯;⊆Gn there exists an undirected graph (V, E) such t...
AbstractWei discovered that the stability number, α(G), of a graph, G, with degree sequence d1, d2,…...
AbstractLet 1≤a<b be integers and G a graph of order n sufficiently large for a and b. Then G has an...
AbstractFor a finite simple graph G, we denote the set of degrees of its vertices, known as its degr...
AbstractWe prove the following theorem: Let G be a graph with vertex-set V and ƒ, g be two integer-v...
AbstractLet a1,a2,…,an and b1,b2,…,bn be integers with 0⩽ai⩽bi for i=1,2,…,n. The purpose of this no...
Let a1,a2,...,an, and b1,b2,...,bn be integers with 0 ≤ ai ≤ bi for i = 1,2,...,n. The purpose of th...
Graph TheoryLet (a1,a2,\textellipsis,an) and (b1,b2,\textellipsis,bn) be two sequences of nonnegativ...
AbstractWe show that the Erdős–Gallai condition characterizing graphical degree sequences of length ...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractLet t(⩾3), a and b be integers with 0⩽a<b. A graph is called K1,t-free if it contains no K1,...
AbstractLet d1, d2, …,dn be the degree sequence of a simple graph and suppose p is a positive intege...
summary:The minimum orders of degree-continuous graphs with prescribed degree sets were investigated...
AbstractLet G be a graph on X, and let f(x), g(x) be positive integers; several authors have given c...
AbstractLet G be a graph of order n, and let a and b be integers such that 1⩽a<b. Then we prove that...
AbstractFor any finite sequence of groups G0⊆G1⊆⋯;⊆Gn there exists an undirected graph (V, E) such t...
AbstractWei discovered that the stability number, α(G), of a graph, G, with degree sequence d1, d2,…...
AbstractLet 1≤a<b be integers and G a graph of order n sufficiently large for a and b. Then G has an...
AbstractFor a finite simple graph G, we denote the set of degrees of its vertices, known as its degr...
AbstractWe prove the following theorem: Let G be a graph with vertex-set V and ƒ, g be two integer-v...
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