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

商学部

研究成果: Article › 査読

3 被引用数 (Scopus)

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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.

本文言語	English
論文番号	013
ジャーナル	Electronic Journal of Combinatorics
巻	22
号	3
DOI	https://doi.org/10.37236/3255
出版ステータス	Published - 2015 7月 17

ASJC Scopus subject areas

理論的コンピュータサイエンス
幾何学とトポロジー
離散数学と組合せ数学
計算理論と計算数学
応用数学

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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

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