The ffamiltonian problem is to determine whether a graph contains a spanning (Hamiltonian) path or cycle. Here we study the Hamiltonian problem for the generalized Fibonacci cubes, which are a new family of graphs that have applications in interconnection topologies [J. Liuand W.-J. Hsu, "Distributed Algorithms for Shortest-Path, Deadlock-Free Routing and Broadcasting in a Class of Interconnection Topologies," International Parallel Processing Symposium (1 99211. We show that each member of this family contains a Hamiltonian path. Furthermore, we also characterize the members of this family that contain a Hamiltonian cycle.
Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree d tree can be found in O(n (log n)d-E) steps. This has applications to integrated circuit layout, in particular the layout of Weinberger arrays [41]. This also .yields an algorithm for determining the black/white pebble demand of degree three trees. We also show that for degree three trees, cutwidth is identical to search number and give a forbidden subgraph characterization of degree three trees having cutwidth k.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.