We present a few results and a larger number of questions concerning partitions of graphs or hypergraphs, where the objective is to maximize or minimize several quantities simultaneously. We consider… (More)

Edwards showed that every graph of size m ≥ 1 has a bipartite subgraph of size at least m/2 + √ m/8 + 1/64− 1/8. We show that every graph of size m ≥ 1 has a bipartition in which the Edwards bound… (More)

Gyárfás and Sumner independently conjectured that for every tree T and integer k there is an integer f(k, T ) such that every graph G with χ(G) > f(k, T ) contains either Kk or an induced copy of T .… (More)

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)}.

A conjecture of Bollob́as and Thomason asserts that, for r ≥ 1, everyr -uniform hypergraph with m edges can be partitioned into r classes such that every class meets at least rm/(2r − 1) edges.… (More)

Alon, Bollobás, Krivelevich and Sudakov [1] proved that every graph with a large cut has a bipartition in which each vertex class contains correspondingly few edges. We prove an analogous result for… (More)