On Generalized Random Railways

HANS GARMO, SVANTE JANSON, MICHA KAROSKI
2004 Combinatorics, probability & computing  
We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches not allowing traffic between any pair of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.
doi:10.1017/s0963548303005820 fatcat:mxvcbasc4neq5nehnsk2m4mmze