Search

Abstract: We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the free groups with finite. [ABSTRACT FROM AUTHOR]

Abstract: We show that the topological space of any infinite graph and its ends is normal. In particular, end spaces themselves are normal. [Copyright &y& Elsevier]

Abstract: Let be an -partite -graph, all of whose sides have the same size . Suppose that there exist two sides of , each satisfying the following condition: the degree of each legal -tuple contained in the complement of this side is strictly larger than . We prove that under this condition must have a perfect matching. This answers a question of Kühn and Osthus. [Copyright &y& Elsevier]

Abstract: Two non-isomorphic graphs are twins if each is isomorphic to a subgraph of the other. We prove that a rayless graph has either infinitely many twins or none. [Copyright &y& Elsevier]

Abstract: We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff''s first law also for ends. [Copyright &y& Elsevier]