TY  - JOUR
A1  - Keller, Matthias
A1  - Münch, Florentin
T1  - A new discrete Hopf-Rinow theorem
T2  - Discrete Mathematics
N2  - We prove a version of the Hopf-Rinow theorem with respect to path metrics on discrete spaces. The novel aspect is that we do not a priori assume local finiteness but isolate a local finiteness type condition, called essentially locally finite, that is indeed necessary. As a side product we identify the maximal weight, called the geodesic weight, generating the path metric in the situation when the space is complete with respect to any of the equivalent notions of completeness proven in the Hopf-Rinow theorem. As an application we characterize the graphs for which the resistance metric is a path metric induced by the graph structure.
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48332
SN  - 0012-365X
SN  - 1872-681X
VL  - 342
IS  - 9
SP  - 2751
EP  - 2757
PB  - Elsevier
CY  - Amsterdam
ER  -