Erdős Problem #842

Let $G$ be a graph on $3n$ vertices formed by taking $n$ vertex disjoint triangles and adding a Hamiltonian cycle (with all new edges) between these vertices. Does $G$ have chromatic number at most $3$?

#842: [Er92b]

graph theory | chromatic number

The answer is yes, proved by Fleischner and Stiebitz [FlSt92].

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T. F. Bloom, Erdős Problem #842, https://www.erdosproblems.com/842, accessed 2025-12-07