Minimum degree conditions for H-linked graphs

New Ore-Type Conditions for H-Linked Graphs

For a fixed (multi)graph H, a graph G is H-linked if any injection f : V (H) → V (G) can be extended to an H-subdivision in G. The notion of an H-linked graph encompasses several familiar graph classes, including k-linked, kordered and k-connected graphs. In this paper, we give two sharp Ore-type degree sum conditions that assure a graph G is H-linked for arbitrary H. These results extend and r...

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

Degree Conditions for H-Linked Digraphs

Given a digraphH, anH-subdivision is any digraph obtained by replacing each arc uv of H with a (directed) u− v path of arbitrary length. A directed graph D is H-linked if every injective functionf : V (H) → V (D) extends to an H-subdivision in G. The H-linkage property has been well-studied in undirected graphs, and in both the directed and undirected case generalizes the notions of k-linked an...

Sufficient conditions for maximally edge-connected and super-edge-connected

Let $G$ be a connected graph with minimum degree $delta$ and edge-connectivity $lambda$. A graph ismaximally edge-connected if $lambda=delta$, and it is super-edge-connected if every minimum edge-cut istrivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree.In this paper, we show that a connected graph or a connected triangle-free graph is maximall...

The irregularity and total irregularity of Eulerian graphs

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.