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A note on high-dimensional discrepancy of subtrees
Lawrence Hollom, Lyuben Lichev, Adva Mond +1
For a tree and a function , the imbalance of a subtree is given by . The -dimensional discrepancy o…
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…
Discrepancies of spanning trees in dense graphs
Lawrence Hollom, Lyuben Lichev, Adva Mond +1
We address several related problems on combinatorial discrepancy of trees in a setting introduced by Erdős, Füredi, Loebl and Sós. Given a fixed tree on vertices and an edg…
A uniform bound on almost colour-balanced perfect matchings in colour-balanced cliques
Lawrence Hollom
An edge-colouring of a graph is said to be colour-balanced if there are equally many edges of each available colour. We are interested in finding a colour-balanced perfect matc…
Almost colour-balanced spanning forests in complete graphs
Lawrence Hollom, Adva Mond, Julien Portier
Given whose edges are coloured red and blue, and a forest of order , we seek embeddings of with small imbalance, that is, difference between the numbers of red and…
The bunkbed conjecture is not robust to generalisation
Lawrence Hollom
The bunkbed conjecture, which has featured in the folklore of probability theory since at least 1985, concerns bond percolation on the product graph . We have two copies…