Journal of the
Korean Mathematical Society JKMS

In this paper we investigate the projections of bouquet graph $B$ with two cycles. A projection of $B$ is said to be trivial if only trivial embeddings are obtained from the projection. It is shown that, to cover all nontrivial projections of $B$, at least three embeddings of $B$ are needed. We also show that a nontrivial projection of $B$ is covered by one of some two embeddings if the image of each cycle has at most one self-crossing.

Keywords: projection of graph, embedding of graph, bouquet graph

MSC numbers: Primary 57M25; Secondary 57M15, 05C10