  The third version of the open-domain dialogue system Alquist developed within
the Alexa Prize 2020 competition is designed to conduct coherent and engaging
conversations on popular topics. The main novel contribution is the
introduction of a system leveraging an innovative approach based on a
conversational knowledge graph and adjacency pairs. The conversational
knowledge graph allows the system to utilize knowledge expressed during the
dialogue in consequent turns and across conversations. Dialogue adjacency pairs
divide the conversation into small conversational structures, which can be
combined and allow the system to react to a wide range of user inputs flexibly.
  We discuss and describe Alquist's pipeline, data acquisition and processing,
dialogue manager, NLG, knowledge aggregation, and a hierarchy of adjacency
pairs. We present the experimental results of the individual parts of the
system.
