A tie-break model for graph search

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.