Moderate -0.8 This is a straightforward recall question testing knowledge of Kuratowski's theorem: any graph containing K₅ as a subgraph is non-planar. It requires only recognition of a standard theorem with no problem-solving or multi-step reasoning, making it easier than average even for Further Maths.
The graph \(G\) has a subgraph isomorphic to \(K_5\), the complete graph with 5 vertices.
Which of the following statements about \(G\) must be true?
Tick \((\checkmark)\) one box.
[1 mark]
\(G\) is not connected
\(G\) is not Hamiltonian
\(G\) is not planar
\(G\) is not simple
The graph $G$ has a subgraph isomorphic to $K_5$, the complete graph with 5 vertices.
Which of the following statements about $G$ must be true?
Tick $(\checkmark)$ one box.
[1 mark]
$G$ is not connected
$G$ is not Hamiltonian
$G$ is not planar
$G$ is not simple
\hfill \mbox{\textit{AQA Further Paper 3 Discrete 2022 Q1 [1]}}