$1($a$)$: We are given a graph G that is connected, bipartite, and each node has an even degree. Show $($prove$)$ that we can colour each edge red or blue so that each node has half of the edges touching it coloured red and

the other half blue.

$1($b$)$: Give an example of a connected graph and each node has an even degree, in which we cannot colour the edges as in part $($a$).$