A fast deterministic detection of small pattern graphs in graphs without large cliques

Research output: Contribution to journalArticle


We show that for several pattern graphs on four vertices (e.g., C4), their induced copies in host graphs with n vertices and no clique on k+1 vertices can be deterministically detected in O(n2.5719k0.3176+n2k2) time for k<n0.394 and O(n2.5k0.5+n2k2) time for k≥n0.394. The aforementioned pattern graphs have a pair of non-adjacent vertices whose neighborhoods are equal. By considering dual graphs, in the same asymptotic time, we can also detect four vertex pattern graphs, that have an adjacent pair of vertices with the same neighbors among the remaining vertices (e.g., K4), in host graphs with n vertices and no independent set on k+1 vertices. By using the concept of Ramsey numbers, we can extend our method for induced subgraph isomorphism to include larger pattern graphs having a set of independent vertices with the same neighborhood and n-vertex host graphs without cliques on k+1 vertices (as well as the pattern graphs and host graphs dual to the aforementioned ones, respectively).


External organisations
  • University of Warsaw
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computer Science


  • Induced subgraph isomorphism, Matrix multiplication, Time complexity, Witnesses for Boolean matrix product
Original languageEnglish
Pages (from-to)79-87
JournalTheoretical Computer Science
Early online date2018 Oct 25
Publication statusPublished - 2019
Publication categoryResearch