Let T be an even subset of the vertices of a graph G. A T-cut is an edge-cutset of the graph which divides T into two odd sets. We prove that if G is bipartite, then the maximum number of disjoint !T-cuts is equal to the minimum cardinality of a set of edges which meets every T-cut. (A weaker form of this was proved by Edmonds and Johnson.) We deduce a solution to the real-valued multi-commodit...

The classical, linear-time solvable Feedback Edge Set problem is concerned with finding a minimum number of edges intersecting all cycles in (static, unweighted) graph. We provide first study this the setting temporal graphs , where are present only at certain points time. find that there four natural generalizations which turn out to be NP-hard. also tractability these problems respect several...

We introduce a new graph-theoretic concept in the area of network monitoring. In this area, one wishes to monitor vertices and/or edges (viewed as graph) order detect and prevent failures. Inspired by two notions studied literature (edge-geodetic sets distance-edge-monitoring sets), we define notion monitoring edge-geodetic set (MEG-set for short) graph G an $$S\subseteq V(G)$$ (that is, every ...

We solve the problem of identifying (reconstructing) network topology from steady state network measurements. Concretely, given only a data matrix X where the Xij entry corresponds to flow in edge i in steady-state j, we wish to find a network structure for which flow conservation is obeyed at all the nodes. This models many network problems involving conserved quantities including water, power...

The purpose of this study was to evaluate the use of diverging-cut aperture to minimize collimator contamination in proton therapy. Two sets of apertures with nondivergent and divergent edge were fabricated to produce a 10 cm × 10 cm field at the radiation isocenter of a single-room proton therapy unit. Transverse profiles were acquired in a scanning water tank with both aperture sets. Up to 9....