  In this paper, we consider the problem of the recognition of various kinds of
orderings produced by graph searches. To this aim, we introduce a new
framework, the Tie-Breaking Label Search (TBLS), in order to handle a broad
variety of searches. This new model is based on partial orders defined on the
label set and it unifies the General Label Search (GLS) formalism of Krueger,
Simonet and Berry (2011), and the "pattern-conditions" formalism of Corneil and
Krueger (2008). It allows us to derive some general properties including new
pattern-conditions (yielding memory-efficient certificates) for many usual
searches, including BFS, DFS, LBFS and LDFS. Furthermore, the new model allows
easy expression of multi-sweep uses of searches that depend on previous
(search) orderings of the graph's vertex set.
