This paper is the second of three parts of a comprehensive survey of a newly emerging field:
a topological approach to the study of locally finite graphs that crucially incorporates their …

Uniqueness of electrical currents in a network of finite total resistance Page 1 J. London Math.
Soc. (2) 82 (2010) 256–272 Cо2010 London Mathematical Society doi:10.1112/jlms/jdq034 …

Let G be a graph each edge e of which is given a length ℓ (e). This naturally induces a
distance d ℓ (x, y) between any two vertices x, y, and we let| G| ℓ denote the completion of …

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This paper is intended as an introductory survey of a newly emerging field: a topological
approach to the study of locally finite graphs that crucially incorporates their ends …

We investigate the end spaces of infinite dual graphs. We show that there exists a natural
homeomorphism* between the end spaces of a graph and its dual, and that* preserves the …

Solving a problem of Diestel [9] relevant to the theory of cycle spaces of infinite graphs, we
show that the Freudenthal compactification of a locally finite graph can have connected …

For graphs F, G, and H, we write F→(G, H) if every red-blue coloring of the edges of F
produces a red copy of G or a blue copy of H. The graph F is said to be (G, H)-minimal if it is …

Bounds on the minimum degree and on the number of vertices attaining it have been much
studied for finite edge-/vertex-minimally k-connected/k-edge-connected graphs. We give an …

We are interested in the relation between the average/minimum degree and the appearance
of substructures in infinite graphs. In finite graphs, the impact of the average degree on the …