 Triangle with an attached leaf in a binomial random graph

Partition the vertices into two sets of comparable size. If $np\to \infty$, the first set contains a triangle with probability tending to one. Conditional on any triangle chosen using only internal edges, the probability that none of its vertices has a neighbour in the second set is at mostHence $G(n,p)$ contains a triangle with an attached leaf with probability tending to one.