Geodesic
Forbidden triples generating a finite set of 3-connected graphs
Yoshimi Egawa1 ; Jun Fujisawa2 ; Michitaka Furuya1 ; Michael D Plummer3 ; Akira Saito4
1Tokyo University of Science
2Keio University
3Vanderbilt University
4Nihon University
The electronic journal of combinatorics, Tome 22 (2015) no. 3
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For a graph $G$ and a set $\mathcal{F}$ of connected graphs, $G$ is said be $\mathcal{F}$-free if $G$ does not contain any member of $\mathcal{F}$ as an induced subgraph. We let $\mathcal{G} _{3}(\mathcal{F})$ denote the set of all $3$-connected $\mathcal{F}$-free graphs. This paper is concerned with sets $\mathcal{F}$ of connected graphs such that $|\mathcal{F}|=3$ and $\mathcal{G} _{3}(\mathcal{F})$ is finite. Among other results, we show that for an integer $m\geq 3$ and a connected graph $T$ of order greater than or equal to $4$, $\mathcal{G} _{3}(\{K_{4},K_{2,m},T\})$ is finite if and only if $T$ is a path of order $4$ or $5$.
DOI : 10.37236/3255
Classification : 05C75
Mots-clés : forbidden subgraph, forbidden triple, \(3\)-connected graph

Yoshimi Egawa  1   ; Jun Fujisawa  2   ; Michitaka Furuya  1   ; Michael D Plummer  3   ; Akira Saito  4

1 Tokyo University of Science
2 Keio University
3 Vanderbilt University
4 Nihon University 
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     author = {Yoshimi Egawa and Jun Fujisawa and Michitaka Furuya and Michael D Plummer and Akira Saito},
     title = {Forbidden triples generating a finite set of 3-connected graphs},
     journal = {The electronic journal of combinatorics},
     year = {2015},
     volume = {22},
     number = {3},
     doi = {10.37236/3255},
     zbl = {1327.05287},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3255/}
}
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Yoshimi Egawa; Jun Fujisawa; Michitaka Furuya; Michael D Plummer; Akira Saito. Forbidden triples generating a finite set of 3-connected graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/3255

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