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Circular-arc graphs are intersection graphs of arcs on the circle. The aim ofour work is to present a polynomial time algorithm testing whether twocircular-arc graphs are isomorphic. To accomplish our task we constructdecomposition trees, which are the structures representing all normalizedintersection models of circular-arc graphs. Normalized models reflect theneighbourhood relation in circular-arc graphs and can be seen as theircanonical representations; in particular, every intersection model can beeasily transformed into a normalized one.  Our work adapts and appropriately extends the previous work on the similartopic done by Hsu [\emph{SIAM J. Comput. 24(3), 411--439, (1995)}]. In hiswork, Hsu developed decomposition trees representing all normalized models ofcircular-arc graphs. However due to the counterexample given in [\emph{DiscreteMath. Theor. Comput. Sci., 15(1), 157--182, 2013}], his decomposition trees cannot be used by algorithms testing isomorphism of circular-arc graphs.

Testing isomorphism of circular-arc graphs -- Hsu's approach revisited