Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox, and Zhao. These inheritance lemmas also imply ...

Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox, and Zhao. These inheritance lemmas also imply ...

Loebl, Komlos and Sos conjectured that every n-vertex graph G with at least n/2 vertices of degree at least k contains each tree T of order k + 1 as a subgraph. We give a sketch of a proof of the approximate version of ...

We consider conditions which allow the embedding of linear hypergraphs of fixed size. In particular, we prove that any k-uniform hypergraph H of positive uniform density contains all linear k-uniform hypergraphs of a given ...

In a series of four papers we prove the following relaxation of the Loebl–Koml ́os–S ́os Con-jecture: For everyα >0 there exists a numberk0such that for everyk > k0everyn-vertexgraphGwith at least (12+α)nvertices of degree ...

This is the second of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph ...

This is the third of a series of four papers in which we prove the following relaxation ofthe Loebl–Komlós–S ́os Conjecture: For everyα >0 there exists a numberk0such that foreveryk > k0everyn-vertex ...

This is the last of a series of four papers in which we prove the following relaxation of the Loebl-Komlós-Sós conjecture: For every α > 0 there exists a number k0 such that for every k > k0, every n-vertex graph G ...

In 1983, Chvatal, Trotter and the two senior authors proved that for any Delta there exists a constant B such that, for any n, any 2-colouring of the edges of the complete graph K(N) with N >= Bn vertices yields a monochromatic ...

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. ...