AbstractLet G be a graph of order n and k any positive integer with k⩽n. It has been shown by Brandt et al. that if |G|=n⩾4k and if the degree sum of any pair of nonadjacent vertices is at least n, then G can be partitioned into k cycles. We prove that if the degree sum of any pair of nonadjacent vertices is at least n−k+1, then G can be partitioned into k subgraphs Hi, 1⩽i⩽k, where Hi is a cycle or K1 or K2, except G=C5 and k=2
Abstract Given k ≥ 1, a k-proper partition of a graph G is a partition P of V (G) such that each par...
AbstractLet G be any graph, and let c(G) denote the circumference of G. If, for every pair c1,c2 of ...
AbstractLet S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees o...
AbstractLet G be a graph of order n and k any positive integer with k⩽n. It has been shown by Brandt...
AbstractLet k,n be integers with 2≤k≤n, and let G be a graph of order n. We prove that if max{dG(x),...
Abstract:Let G be a graph of order n and k be any positive integer with 2 ≤k ≤ n. In this paper, we ...
AbstractLet G be a graph of order n and k a positive integer. A set of subgraphs H={H1,H2,…,Hk} is c...
AbstractLet G be a graph of order at least 3k, where k is a positive integer. Justesen (Ann. Disc. M...
AbstractLet G be a graph of order n and k a positive integer. A set of subgraphs H={H1,H2,…,Hk} is c...
AbstractLet k⩾1 be an integer and G be a graph of order n⩾3k satisfying the condition that σ2(G)⩾n+k...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractFor a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. Su...
AbstractFan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187...
AbstractWe give an alternative proof of a conjecture due to Wang (J. Graph Theory 26 (1997) 105) in ...
Abstract Given k ≥ 1, a k-proper partition of a graph G is a partition P of V (G) such that each par...
AbstractLet G be any graph, and let c(G) denote the circumference of G. If, for every pair c1,c2 of ...
AbstractLet S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees o...
AbstractLet G be a graph of order n and k any positive integer with k⩽n. It has been shown by Brandt...
AbstractLet k,n be integers with 2≤k≤n, and let G be a graph of order n. We prove that if max{dG(x),...
Abstract:Let G be a graph of order n and k be any positive integer with 2 ≤k ≤ n. In this paper, we ...
AbstractLet G be a graph of order n and k a positive integer. A set of subgraphs H={H1,H2,…,Hk} is c...
AbstractLet G be a graph of order at least 3k, where k is a positive integer. Justesen (Ann. Disc. M...
AbstractLet G be a graph of order n and k a positive integer. A set of subgraphs H={H1,H2,…,Hk} is c...
AbstractLet k⩾1 be an integer and G be a graph of order n⩾3k satisfying the condition that σ2(G)⩾n+k...
AbstractLet G be a graph. For S⊂V(G), let Δk(S) denote the maximum value of the degree sums of the s...
AbstractEl-Zahar (1984) conjectured that if G is a graph on n1+n2+⋯+nk vertices with ni⩾3 for 1⩽i⩽k ...
AbstractFor a graph G, let σ2(G) denote the minimum degree sum of a pair of nonadjacent vertices. Su...
AbstractFan [G. Fan, Distribution of cycle lengths in graphs, J. Combin. Theory Ser. B 84 (2002) 187...
AbstractWe give an alternative proof of a conjecture due to Wang (J. Graph Theory 26 (1997) 105) in ...
Abstract Given k ≥ 1, a k-proper partition of a graph G is a partition P of V (G) such that each par...
AbstractLet G be any graph, and let c(G) denote the circumference of G. If, for every pair c1,c2 of ...
AbstractLet S be a set of vertices of a k-connected graph G. We denote the smallest sum of degrees o...
DOI
Add to ORKG