Forbidden triples generating a finite set of 3-connected graphs

Yoshimi Egawa, Michitaka Furuya, Jun Fujisawa, Michael D. Plummer, Akira Saito

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1 Citation (Scopus)

Abstract

For a graph G and a set F of connected graphs, G is said be F-free if G does not contain any member of F as an induced subgraph. We let G<inf>3</inf> (F) denote the set of all 3-connected F-free graphs. This paper is concerned with sets F of connected graphs such that |F| = 3 and G<inf>3</inf>(F) is finite. Among other results, we show that for an integer m ≥ 3 and a connected graph T of order greater than or equal to 4, G<inf>3</inf>({K<inf>4</inf>,K<inf>2,m</inf>, T}) is finite if and only if T is a path of order 4 or 5.

Original languageEnglish
Article number013
JournalElectronic Journal of Combinatorics
Volume22
Issue number3
Publication statusPublished - 2015 Jul 17

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Keywords

  • 3-connected graph
  • Forbidden subgraph
  • Forbidden triple

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Egawa, Y., Furuya, M., Fujisawa, J., Plummer, M. D., & Saito, A. (2015). Forbidden triples generating a finite set of 3-connected graphs. Electronic Journal of Combinatorics, 22(3), [013].