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  1. Home > Articles & Issues >
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  3. A polynomial bound o ...
Article

A polynomial bound on the number of minimal separators and potential maximal cliques in $P_6$-free graphs of bounded clique number

Marcin Pilipczuk, Paweł Rzążewski
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Submitted on
October 19, 2023
Accepted on
March 12, 2025
Published on
March 18, 2025
Last modified on
March 27, 2025
Volume 27
vol. 27:2
Graph Theory
DOI
10.46298/dmtcs.12438
License
Attribution 4.0 International (CC BY 4.0)
European Commission
948057
Decomposition methods for discrete problems
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1065
Views
751
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A polynomial bound on the number of minimal separators and potential maximal cliques in $P_6$-free graphs of bounded clique number

Marcin Pilipczuk, Paweł Rzążewski
Abstract
In this note we show a polynomial bound on the number of minimal separators and potential maximal cliques in $P_6$-free graphs of bounded clique number.
Keywords
  • Computer Science - Discrete Mathematics
  • Mathematics - Combinatorics
Mathematics Subject Classification 2020
  • 05C75 - Structural characterization of families of graphs
  • 05C85 - Graph algorithms (graph-theoretic aspects)
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