One of the most important sets associated with a poset P is its set of linear extensions, E(P). In this paper, we present an algorithm to generate all of the linear extensions of a poset in constant amortized time; that is, in time O(e(P)), where e(P) = jE(P)j. The fastest previously known algorithm for generating the linear extensions of a poset runs in time O(n e(P)), where n is the number of elements of the poset. Our algorithm is the rst constant amortized time algorithm for generating a \naturally de ned" class of combinatorial objects for which the corresponding counting problem is #P-complete. Furthermore, we show that linear extensions can be generated in constant amortized time where each extension di ers from its predecessor by one or two adjacent transpositions. The algorithm is practical and can be modi ed to e ciently count linear extensions, and to compute P (x < y), for all pairs x; y, in time O(n 2 + e(P)).

The class of cographs, or complement-reducible graphs, arises naturally in many different areas of applied mathematics and computer science. In this paper, we present an optimal algorithm for determining a minimum path cover for a cograph G. In case G has a Harniltonian path (cycle) our algorithm exhibits the path (cycle) as well.

No abstract

No abstract

Every connected simple graph $G$ has an acyclic orientation. Define a graph ${AO}(G)$ whose vertices are the acyclic orientations of $G$ and whose edges join orientations that differ by reversing the direction of a single edge. It was known previously that ${AO}(G)$ is connected but not necessarily Hamiltonian. However, Squire proved that the square ${AO}(G)^2$ is Hamiltonian. We prove the slightly stronger result that the prism ${AO}(G) \times e$ is Hamiltonian. If $G$ is a mixed graph (some edges directed, but not necessarily all), then ${AO}(G)$ can be defined as before. The graph ${AO}(G)$ is again connected but we give examples showing that the prism is not necessarily Hamiltonian.