12 papers
The structure of FAC posets and the Aharoni--Korman conjecture
Lawrence Hollom
A poset is said to satisfy the finite antichain condition, or FAC for short, if it has no infinite antichain. Such posets exhibit rich and complex structure, and it was conject…
The Aharoni--Korman conjecture is false
Lawrence Hollom
A poset is said to satisfy the finite antichain condition, or FAC, if it has no infinite antichain. It was conjectured by Aharoni and Korman in 1992 that any FAC poset poss…
Hypercube geodesics with few colour changes
Lawrence Hollom
What is the maximum, over all 2-colourings of the edges of the -dimensional hypercube , of the minimal number of times a path between a vertex and its antipode $\bar{v}…
Uniformly balanced -factors in multicoloured complete graphs
Agnijo Banerjee, Lawrence Hollom
A balanced colouring of a graph is one in which every colour appears the same number of times. Given a fixed graph on vertices and a balanced -colouring of the complete…
Counterexamples to conjectures on strong maximality and minimality
Lawrence Hollom, Benedict Randall Shaw
We provide counterexamples to several conjectures concerning strongly maximal and strongly minimal structures in infinite graphs and hypergraphs. In particular, we construct 3-unif…
Reverse Littlewood--Offord problems with parity conditions
Lawrence Hollom, Gregory B. Sorkin
We consider the probability that the random signed sum lies within a given distance of the origin, where are fi…