Minimum balanced bipartitions of f-graphs

On minimum balanced bipartitions of triangle-free graphs

Balanced judicious bipartitions of graphs

A bipartition of the vertex set of a graph is called balanced if the sizes of the sets in the bipartition differ by at most one. Bollobás and Scott [3] conjectured that if G is a graph with minimum degree at least 2 then V (G) admits a balanced bipartition V1, V2 such that for each i, G has at most |E(G)|/3 edges with both ends in Vi. The minimum degree condition is necessary, and a result of B...

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...

A note on balanced bipartitions

A balanced bipartition of a graph G is a bipartition V1 and V2 of V (G) such that −1 ≤ |V1| − |V2| ≤ 1. Bollobás and Scott conjectured that if G is a graph with m edges and minimum degree at least 2 then G admits a balanced bipartition V1, V2 such that max{e(V1), e(V2)} ≤ m/3, where e(Vi) denotes the number of edges of G with both ends in Vi. In this note, we prove this conjecture for graphs wi...

Further results on total mean cordial labeling of graphs

A graph G = (V,E) with p vertices and q edges is said to be a total mean cordial graph if there exists a function f : V (G) → {0, 1, 2} such that f(xy) = [(f(x)+f(y))/2] where x, y ∈ V (G), xy ∈ E(G), and the total number of 0, 1 and 2 are balanced. That is |evf (i) − evf (j)| ≤ 1, i, j ∈ {0, 1, 2} where evf (x) denotes the total number of vertices and edges labeled with x (x = 0, 1, 2). In thi...