A min-max theorem for LIFO-search

Archontia C. Giannopoulou, Dimitrios M. Thilikos

Research output: Contribution to journalArticlepeer-review


We introduce a variant of the classic node search game called LIFO-search where searchers are assigned different numbers. The additional rule is that a searcher can be removed only if no searchers of lower rank are in the graph at that moment. We introduce the notion of shelters in graphs and we prove a min-max theorem implying their equivalence with the tree-depth parameter. As shelters provide escape strategies for the fugitive, this implies that the LIFO-search game is monotone and that the LIFO-search parameter is equivalent with the one of tree-depth.

Original languageEnglish (US)
Pages (from-to)395-400
Number of pages6
JournalElectronic Notes in Discrete Mathematics
StatePublished - Dec 1 2011


  • Graph Searching
  • Obstructions
  • Tree-depth
  • Width Parameters

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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