Essential obstacles to Helly circular-arc graphs

A Helly circular-arc graph is the intersection of a set arcs on circle having property. We introduce essential obstacles, which are refinement notion and prove that obstacles precisely minimal forbidden induced subgraphs for class graphs. show it possible to find in linear time, any given obstacle, some subgraph graphs contained as an subgraph. Moreover, relying existing linear-time algorithm finding graphs, we conclude time obstacle not graph. The problem characterization, restricted only remains unresolved. As partial answer this problem, characterization containing no claw 5-wheel. Furthermore, there finding, graph, isomorphic claw, 5-wheel, or