Forbidden triples generating a finite set of 3-connected graphs

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

doi:10.37236/3255

Forbidden triples generating a finite set of 3-connected graphs

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

Faculty of Business and Commerce

Research output: Contribution to journal › Article › peer-review

3 Citations (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 G₃ (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 G₃(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, G₃({K₄,K_2,m, T}) is finite if and only if T is a path of order 4 or 5.

Original language	English
Article number	013
Journal	Electronic Journal of Combinatorics
Volume	22
Issue number	3
DOIs	https://doi.org/10.37236/3255
Publication status	Published - 2015 Jul 17

Keywords

3-connected graph
Forbidden subgraph
Forbidden triple

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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title = "Forbidden triples generating a finite set of 3-connected graphs",

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 G3 (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 G3(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, G3({K4,K2,m, T}) is finite if and only if T is a path of order 4 or 5.",

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T1 - Forbidden triples generating a finite set of 3-connected graphs

AU - Egawa, Yoshimi

AU - Furuya, Michitaka

AU - Fujisawa, Jun

AU - Plummer, Michael D.

AU - Saito, Akira

PY - 2015/7/17

Y1 - 2015/7/17

N2 - 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 G3 (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 G3(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, G3({K4,K2,m, T}) is finite if and only if T is a path of order 4 or 5.

AB - 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 G3 (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 G3(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, G3({K4,K2,m, T}) is finite if and only if T is a path of order 4 or 5.

KW - 3-connected graph

KW - Forbidden subgraph

KW - Forbidden triple

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Forbidden triples generating a finite set of 3-connected graphs

Abstract

Keywords

ASJC Scopus subject areas

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