A branch connection rule of one-way rail network

08/19/2023

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by   Dai Akita, et al.

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We deal with network inspired by toy train, which is constructed by connecting Y-shaped branches. A train passes a branch through either of splitted rails and not allowed to go backward. Under these assumptions, we consider unidirectionality of a rail network, that is, there is a orientation of the rail network such that any trail of a train starting with the direction does not contradict to the orientation. We find that a rail network is one-way if and only if a digraph derived from the rail network is disconnected, which is also equal to no existence of cycle which contains odd number of tracks connecting the same side of branches.