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5 papers · 2 filters
Decompositions into subgraphs of small diameter
Jacob Fox, Benny Sudakov
We investigate decompositions of a graph into a small number of low diameter subgraphs. Let P(n,ε,d) be the smallest k such that every graph G=(V,E) on n vertices has an edge parti…
Enumeration of non-crossing pairings on bit strings
Todd Kemp, Karl Mahlburg, Amarpreet Rattan +1
A non-crossing pairing on a bitstring matches 1s and 0s in a manner such that the pairing diagram is nonintersecting. By considering such pairings on arbitrary bitstrings $1^{n_1}…
Paths and stability number in digraphs
Jacob Fox, Benny Sudakov
The Gallai-Milgram theorem says that the vertex set of any digraph with stability number k can be partitioned into k directed paths. In 1990, Hahn and Jackson conjectured that this…
Large almost monochromatic subsets in hypergraphs
David Conlon, Jacob Fox, Benny Sudakov
We show that for all and there is a constant such that every -coloring of the triples of an -element set contains a subset of size $c\sqrt…
A note on embedding hypertrees
Po-Shen Loh
A classical result from graph theory is that every graph with chromatic number χ> t contains a subgraph with all degrees at least t, and therefore contains a copy of every t-edge t…