  Let $V_{8}+e$ denote the unique graph obtained from the Wagner graph, also
known as $V_{8}$, by adding an edge between two vertices of distance 3 on the
Hamilton cycle, which is exactly a split of a minor of the Petersen graph. A
complete characterization of all internally 4-connected graphs with no $V_{8}$
minor is given in [J. Maharry and N. Robertson, The structure of graphs not
topologically containing the Wagner graph, J. Combin. Theory Ser. B 121 (2016)
398-420]. In this paper we characterize all internally 4-connected graphs with
no $V_{8}+e$ minor.
