Ben Barber, Stefan Glock, Daniela Kühn, Allan Lo, Richard Montgomery, Deryk Osthus Random Struct Alg. 2020; 57: 47– 63. https://doi.org/10.1002/rsa.20915 In Edge decompositions of graphs with high minimum degree, Daniela Kühn, Allan Lo, Deryk Osthus and I proved that the edge sets of sufficiently dense graphs satisfying necessary divisibility conditions could be partitioned into copies of …

# Tag: decompositions

## Clique decompositions of multipartite graphs and completion of Latin squares

Ben Barber, Daniela Kühn, Allan Lo, Deryk Osthus and Amelia Taylor, Journal of Combinatorial Theory, Series A, Volume 151, October 2017, Pages 146–201 PDF A Latin square of order is an grid of cells, each of which contains one of distinct symbols, such that no symbol appears twice in any row or column. There is a natural …

## Fractional clique decompositions of dense graphs and hypergraphs

Ben Barber, Daniela Kühn, Allan Lo, Richard Montgomery and Deryk Osthus, Journal of Combinatorial Theory, Series B, Volume 127, November 2017, Pages 148–186 PDF Together with Daniela Kühn, Allan Lo and Deryk Osthus I proved that for every graph there is a constant such that every “-divisible” graph on vertices with minimum degree at least has an …

## Edge-decompositions of graphs with high minimum degree

Ben Barber, Daniela Kühn, Allan Lo and Deryk Osthus, Advances in Mathematics, Volume 288, 22 January 2016, Pages 337–385 PDF When can the edge set of a graph be partitioned into triangles? Two obvious necessary conditions are that the total number of edges is divisible by 3 and the degree of every vertex is even. We …