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

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceeding


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 time Õ (nωkμ + n2k2), where Õ (f) stands for O(f(log f)c) for some constant c, and μ ≈ 0. 46530. 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 nvertex 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
Title of host publicationWALCOM: Algorithms and Computation - 11th International Conference and Workshops, WALCOM 2017, Proceedings
Number of pages11
Volume10167 LNCS
ISBN (Print)9783319539249
Publication statusPublished - 2017
Publication categoryResearch
Event11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017 - Hsinchu, Taiwan, Province of China
Duration: 2017 Mar 292017 Mar 31

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10167 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349


Conference11th International Conference and Workshops on Algorithms and Computation, WALCOM 2017
CountryTaiwan, Province of China