Let H be a graph. We show that there exists n 0 = n 0 (H) such that for every n n 0 , there is a covering of the edges of K n with copies of H where every edge is covered at most twice and any two copies intersect in at most one edge. Furthermore, the covering we obtain is asymptotically optimal.

Let G be a graph and T a set of vertices. A T -path in G is a path that begins and ends in T , and none of its internal vertices are contained in T . We define a T -path covering to be a union of vertex-disjoint T paths spanning all of T . Concentrating on graphs that are tough (the removal of any nonempty set X of vertices yields at most |X| components), we completely characterize the edges th...

The construction of probabilistic models that can represent large systems requires the ability to describe repetitive and hierarchical structures. To do so, one can resort to constructs from description logics. In this paper we present a class of relational Bayesian networks based on the popular description logic DL-Lite. Our main result is that, for this modeling language, marginal inference a...

SolC. P. and T. Zaslavsky, The covering radius of the cycle code of a graph, Discrete Applied Mathematics 45 (I 993) 63-70. The cycle code of a graph is the binary linear span of the characteristic vectors of circuits. We exploit a connection between the covering radius of this code and minimum T-joins. We obtain a lower bound on the covering radius which is met with equality when the graph is ...

for a given hypergraph $h$ with chromatic number $chi(h)$ and with no edge containing only one vertex, it is shown that the minimum number $l$ for which there exists a partition (also a covering) ${e_1,e_2,ldots,e_l}$ for $e(h)$, such that the hypergraph induced by $e_i$ for each $1leq ileq l$ is $k$-colorable, is $lceil log_{k} chi(h) rceil$.

We investigate the effect of certain natural connectivity constraints on the parameterized complexity of two fundamental graph covering problems, namely k-VERTEX COVER and k-EDGE COVER. Specifically, we impose the additional requirement that each connected component of a solution have at least t vertices (resp. edges from the solution), and call the problem t-TOTAL VERTEX COVER (resp. t-TOTAL E...

In this paper we are interested in algorithms for finding 2-factors that cover certain prescribed edge-cuts in bridgeless cubic graphs. We present an algorithm for finding a minimum-weight 2-factor covering all the 3-edge cuts in weighted bridgeless cubic graphs, together with a polyhedral description of such 2-factors and that of perfect matchings intersecting all the 3-edge cuts in exactly on...