On end-vertices of Lexicographic Breadth First Searches
Discrete Applied Mathematics
A General Label Search to investigate classical graph search algorithms
Discrete Applied Mathematics
A simple algorithm to generate the minimal separators and the maximal cliques of a chordal graph
Information Processing Letters
Distributed computing of efficient routing schemes in generalized chordal graphs
Theoretical Computer Science
Moplex orderings generated by the LexDFS algorithm
Discrete Applied Mathematics
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Graph searching is perhaps one of the simplest and most widely used tools in graph algorithms. Despite this, few theoretical results are known about the vertex orderings that can be produced by a specific search algorithm. A simple characterizing property, such as is known for LexBFS, can aid greatly in devising algorithms, writing proofs of correctness, and showing impossibility results. This paper unifies our view of graph search algorithms by showing simple, closely related characterizations of various well-known search paradigms, including BFS and DFS. Furthermore, these characterizations naturally lead to other search paradigms, namely, maximal neighborhood search and LexDFS.