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- Title
Forbidden Triples Containing a Complete Graph and a Complete Bipartite Graph of Small Order.
- Authors
Egawa, Yoshimi; Furuya, Michitaka
- Abstract
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 $${\mathcal{F}}$$ contains no star, $${|\mathcal{F}|=3}$$ and $${\mathcal{G}_{3}(\mathcal{F})}$$ is finite. Among other results, we show that for a connected graph T( ≠ K) which is not a star, $${\mathcal{G}_{3}(\{K_{4},K_{2,2},T\})}$$ is finite if and only if T is a path of order at most 6.
- Subjects
MONADS (Mathematics); COMPLETE graphs; BIPARTITE graphs; SET theory; MATHEMATICAL models
- Publication
Graphs & Combinatorics, 2014, Vol 30, Issue 5, p1149
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-013-1334-8