Let us denote by $c(G)$ the number of components of graph $G$.
Theory: For a hamiltonain graph we have $c(G-S)\leq|S|$ for any set $S$ of vertices of $G$.
How can I show that Herschel graph is nonhamiltonian using this theory?
2026-03-28 20:54:05.1774731245
Prove Herschel graph is nonhamiltonian
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In fact, this theory can be used to prove that the Herschel graph is non-Hamiltonian.
Let us remove three vertices of this graph lying on its vertical axis of symmetry. We obtain a new graph of two components, each component is a claw ($K_{1,3}$).
Now delete the central vertices of the claws. We will get $6$ of isolated vertices, but we have removed only $5$ of vertices.