Joint Reliability Importance (JRI) is a measurement of the degree of interactions between two components in a system. The value of JRI is non-positive (non-negative) if and only if one component becomes more important when the other has failed (is functioning). In this paper, we study the properties of JRI of the k-out-of-n system, where the system works if there are at least k functioning comp...

An old conjecture by Jünger, Reinelt and Pulleyblank states that every 2-edgeconnected planar graph can be decomposed into paths of length 3 and triangles, provided its size is divisible by 3. We prove the conjecture for a class of planar graphs including all 2-edge-connected series-parallel graphs. We also present a 2edge-connected non-planar graph that can be embedded on the torus and admits ...

We provide the basics of a 2-dimensional theory of automata on series-parallel biposets. We define recognizable, regular and rational sets of series-parallel biposets and study their relationship. Moreover, we relate these classes to languages of series-parallel biposets definable in monadic second-order logic.

A path cover is a decomposition of the edges of a graph into edge-disjoint simple paths. Gallai conjectured that every connected n-vertex graph has a path cover with at most dn/2e paths. We prove Gallai’s conjecture for series-parallel graphs. For the class of planar 3-trees we show how to construct a path cover with at most b5n/8c paths, which is an improvement over the best previously known b...

In this paper, we describe the circuit polytope on series-parallel graphs. We first show the existence of a compact extended formulation. Though not being explicit, its construction process helps us to inductively provide the description in the original space. As a consequence, using the link between bonds and circuits in planar graphs, we also describe the bond polytope on series-parallel graphs.

A parallel constrained coding scheme is considered where p blocks of raw data are encoded simultaneously into q tracks such that the contents of each track belong to a given constraint S It is shown that as q increases there are parallel block decodable encoders for S whose coding ratio p q converges to the capacity of S Examples are provided where parallel coding allows block decodable encoder...

The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem [12], where both the plant and the controllers are modelled as Zielonka automata [13,1] and the controllers have causal memory is a challenging open problem [8,9]. There exists three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when...

It is easy to characterize graphs with no Kk-minors for any integer k ≤ 4, as follows. For k = 1, 2, the problem must be trivial, and for k = 3, 4, those graphs are forests and series-parallel graphs (i.e., graphs obtained from K3 by a sequence of replacing a vertex of degree 2 with a pair of parallel edges, or its inverse operation.) Moreover, Wagner formulated a fundamental characterization o...

In this paper we show that every 3-connected (3-edge-connected) planar graph contains a 2-connected (respectively, 2-edge-connected) spanning partial 2-tree (seriesparallel) graph. In contrast, a recent result by [4] implies that not all 3-connected graphs contain 2-edge-connected series-parallel spanning subgraphs.