We compute a canonical circular-arc representation for a given circular-arc
(CA) graph which implies solving the isomorphism and recognition problem for
this class. To accomplish this we split the class of CA graphs into uniform and
non-uniform ones and employ a generalized version of the argument given by
K\"obler et al (2013) that has been used to show that the subclass of Helly CA
graphs can be canonized in logspace. For uniform CA graphs our approach works
in logspace and in addition to that Helly CA graphs are a strict subset of
uniform CA graphs. Thus our result is a generalization of the canonization
result for Helly CA graphs. In the non-uniform case a specific set of ambiguous
vertices arises. By choosing the parameter to be the cardinality of this set
the obstacle can be solved by brute force. This leads to an O(k + log n) space
algorithm to compute a canonical representation for non-uniform and therefore
all CA graphs.Comment: 14 pages, 3 figure
