Strict confluent graphs are placed inside string graphs, unit interval graphs inside strict confluent graphs, strict bipartite outerconfluent graphs are exactly the domino-free bipartite permutation graphs, and strict outerconfluent graphs have cop number two.
Congressus Numerantium 58, 165–174 (1987)
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On Strict (Outer-)Confluent Graphs
Strict confluent graphs are placed inside string graphs, unit interval graphs inside strict confluent graphs, strict bipartite outerconfluent graphs are exactly the domino-free bipartite permutation graphs, and strict outerconfluent graphs have cop number two.