Recognition of generalized search trees on unresolved graph classes

Determine the complexity of generalized search-tree recognition for Breadth First Search on chordal graphs and for Lexicographic Depth First Search, Maximum Cardinality Search, and Maximal Neighborhood Search on bipartite and chordal bipartite graphs.

Background

The paper establishes the complexity of generalized search-tree recognition for several common graph searches and graph classes, including completeness results on general graphs and polynomial-time algorithms on selected bipartite and chordal settings. The conclusion identifies the remaining cases of Breadth First Search on chordal graphs and Lexicographic Depth First Search, Maximum Cardinality Search, and Maximal Neighborhood Search on bipartite-related graph classes as unresolved.