Stars in forbidden triples generating a finite set of graphs with minimum degree four

Kotani, Takafumi (Tokyo University of Science)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

For a family H of graphs, a graph G is said to be H-free if G contains no member of H as a induced subgraph. Let G4(H) denote the family of connected H-free graphs having minimum degree at least 4. In this paper, we characterize the families H of connected graphs with |H|=3 such that H contains a star and G4(H) is a finite family, except for the case where {K4, K1, n}⊆H with 3 ≤ n ≤ 4.