{c}

\b[False.] A connected graph has an <Eulerian cycle> exactly when every vertex has even degree. In $K_n$ every degree is $n-1$, so it has an <Eulerian cycle> precisely when $n$ is odd. The <complete graph> $K_4$ is a counterexample to the statement for all $n\geq3$.

Solution

Past exam of the probability, statistics and options I course of the University of Oxford / 2007 / R / 1 / i / Solution

 Solution (source code)