A degree condition implying Ore-type condition for even [2,b]-factors in graphs

Ore-type degree condition for heavy paths in weighted graphs

A weighted graph is one in which every edge e is assigned a nonnegative number w(e), called the weight of e. For a vertex v of a weighted graph, d(v) is the sum of the weights of the edges incident to v. And the weight of a path is the sum of the weights of the edges belonging to it. In this paper, we give a sufficient condition for a weighted graph to have a heavy path which joins two specifie...

Ore-type degree condition of supereulerian digraphs

A digraph D is supereulerian if D has a spanning directed eulerian subdigraph. Hong et al. proved that δ(D) + δ(D) ≥ |V (D)| − 4 implies D is supereulerian except some well-characterized digraph classes if the minimum degree is large enough. In this paper, we characterize the digraphs D which are not supereulerian under the condition d+D (u) + d−D (v) ≥ |V (D)| − 4 for any pair of vertices u an...

An Ore-type condition for arbitrarily vertex decomposable graphs

Let G be a graph of order n and r , 1 ≤ r ≤ n, a fixed integer. G is said to be r -vertex decomposable if for each sequence (n1, . . . , nr ) of positive integers such that n1 + · · · + nr = n there exists a partition (V1, . . . , Vr ) of the vertex set of G such that for each i ∈ {1, . . . , r}, Vi induces a connected subgraph of G on ni vertices. G is called arbitrarily vertex decomposable if...

A Degree Condition For Graphs to Have Connected (g, f)-Factors

On graphs satisfying a local ore-type condition

For an integer i, a graph is called an Li-graph if, for each triple of vertices u, v, w with d(u, v) = 2 and w ∈ N(u) ∩N(v), d(u) + d(v) ≥ |N(u) ∪N(v) ∪N(w)| − i. Asratian and Khachatrian proved that connected L0-graphs of order at least 3 are hamiltonian, thus improving Ore’s Theorem. All K1,3-free graphs are L1-graphs, whence recognizing hamiltonian L1-graphs is an NP-complete problem. The fo...