8 papers · 1 filter
Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings
Michelle Delcourt, Luke Postle
In 1973, Erdős conjectured the existence of high girth -Steiner systems. Recently, Glock, Kühn, Lo, and Osthus and independently Bohman and Warnke proved the approximate v…
Acyclic List Colouring Locally Planar Graphs
Luke Postle, Evelyne Smith-Roberge, Massimo Vicenzo
A (vertex) colouring of graph is \emph{acyclic} if it contains no bicoloured cycle. In 1979, Borodin proved that planar graphs are acyclically 5-colourable. In 2010, Kawarabayashi…
On generalized Ramsey numbers in the non-integral regime
Patrick Bennett, Michelle Delcourt, Lina Li +1
A -coloring of a graph is an edge-coloring of such that every -clique receives at least colors. In 1975, ErdÅs and Shelah introduced the generalized Ramsey n…
Fractional coloring with local demands and applications to degree-sequence bounds on the independence number
Tom Kelly, Luke Postle
In a fractional coloring, vertices of a graph are assigned measurable subsets of the real line and adjacent vertices receive disjoint subsets; the fractional chromatic number of a…
Reducing Linear Hadwiger's Conjecture to Coloring Small Graphs
Michelle Delcourt, Luke Postle
In 1943, Hadwiger conjectured that every graph with no minor is -colorable for every . In the 1980s, Kostochka and Thomason independently proved that every gra…
Clique Decompositions in Random Graphs via Refined Absorption
Michelle Delcourt, Tom Kelly, Luke Postle
We prove that if for some , then asymptotically almost surely the binomial random graph has a -packing containing all but at most $n…