We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...

We introduce the simple extension complexity of a polytope P as the smallest number of facets of any simple (i.e., non-degenerate in the sense of linear programming) polytope which can be projected onto P . We devise a combinatorial method to establish lower bounds on the simple extension complexity and show for several polytopes that they have large simple extension complexities. These example...

We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function. The algorithm is based on a recursive characterization of clique trees, and it runs in O(4) time for n vertices. On an eight-vertex benchmark instance, our implementation turns out to be about ten million times faster than a recently proposed, constraint satisfaction based algori...

We consider a graph Ln, with n even, which is a complete graph with an additional loop at each vertex and minus 1-factor and we prove that it is edge-disjointly decomposable into closed trails of even lengths greater than four, whenever these lengths sum up to the size of the graph Ln. We also show that this statement remains true if we remove from Ln two loops attached to nonadjacent vertices....

We characterize the graphs that admit a decomposition into circuits, i.e. finite or infinite connected 2-regular graphs. Moreover, we show that, as is the case for the removal of a closed eulerian subgraph from a finite graph, removal of a non-dominated eulerian subgraph from a (finite or infinite) graph does not change its circuit-decomposability or circuit-indecomposability. For cycle-decompo...

A cycle in a multipartite graph G is gregarious if it contains at most one vertex from each partite set of G. The complete n-partite graph with partite sets of size m, denoted by Kn(m) is shown to have a decomposition into gregarious 4-cycles. The notion of a gregarious 4-cycle decomposition of this type was introduced in [3]. A 4-cycle decomposition of Kn(m) is circular if it is it is invarian...

Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (...

We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable, and thus shellable, sphere. In particular, this implies a positivity result for Schubert polynomials. Mor...