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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Kotani, Takafumi
Tokyo University of Science
Electrical & Electronics Engineering

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Stars in forbidden triples generating a finite set of graphs with minimum degree four Kotani, Takafumi
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.1.1

Abstract

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.
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