Complex sentence: Arkansas and LSU had enjoyed a neighboring-state rivalry beginning in 1901, however, the two teams had not met since 1936, the end of a 23-year run of meetings in Shreveport.
Split into simpler sentences: Arkansas and LSU had enjoyed a neighboring-state rivalry beginning in 1901. The two teams had not met since 1936, the end of a 23-year run of meetings in Shreveport.