Balanced judicious bipartitions of graphs

Judicious partitions of bounded-degree graphs

We prove results on partitioning graphs G with bounded maximum degree. In particular, we provide optimal bounds for bipartitions V (G) = V1 ∪ V2 in which we minimize max{e(V1), e(V2)}.

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.

On minimum balanced bipartitions of triangle-free graphs

Judicious partitions of directed graphs

The area of judicious partitioning considers the general family of partitioning problems in which one seeks to optimize several parameters simultaneously, and these problems have been widely studied in various combinatorial contexts. In this paper, we study essentially the most fundamental judicious partitioning problem for directed graphs, which naturally extends the classical Max Cut problem ...

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...