A note on balanced bipartitions

Multipartite entanglement in qubit systems

We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally multipartite entangled states. They have a bipartite entanglement that does not depend on the bipartition and is maximal for all possible biparti...

On minimum balanced bipartitions of triangle-free graphs

Minimum balanced bipartitions of f-graphs

In this paper, we show that each f -graph with more than 5 vertices has an unique minimum bipartition, and we also show the upper and lower bound of the balanced size of f -graphs.

A note on vague graphs

In this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. Also, density and balanced irregular vague graphs are discussed and some of their properties are established. Finally we give an application of vague digraphs.

Efficient Network Flow Based Ratio-Cut Netlist Hypergraph Partitioning

We present a new efficient heuristic that finds good ratio-cut bipartitions of hypergraphs that model large VLSI netlists. Ratio cut measure is given by the ratio of the number of nets cut between two blocks and the product of the cardinality (size) of each block. Hypergraphs model VLSI netlists in a more natural fashion than do graphs. Our new heuristic may be considered a hybrid between the a...