Stack and Queue Layouts of Halin Graphs

A Halin graph the union of a tree with no degree-2 vertices and a cycle on the leaves of the tree. This paper examines the problem of laying out Halin graphs using stacks and queues. A k-stack (k-queue) layout of a graph consists of a linear ordering of the vertices along with an assignment of each edge to one of k stacks (queues). The ordering and the edge assignments must be made such that if the ordering is traversed from left to right, then each edge can be placed in its assigned stack (queue) when its left endpoint is encountered and removed from its assigned stack (queue) when its right endpoint is encountered. In this paper it is proven that 2 stacks are necessary and su cient, and that 2 queues are necessary and 3 queues are su cient, to lay out every Halin graph,