3 citations · 11 across the 24 of their papers we have counts for
62 papers · 1 filter
Long Directed Cycles in Vertex-Transitive Digraphs
Bowen Li, Abhishek Methuku
The search for Hamiltonian cycles in vertex-transitive graphs and digraphs is a classical problem at the interface of graph theory and group theory. In the undirected setting, this…
List coloring uncrowded hypergraphs at the shattering threshold
Abhishek Dhawan, Abhishek Methuku, Minh-Quan Vo
Improving an earlier bound of Frieze and Mubayi, Iliopoulos showed that any -uniform uncrowded hypergraph of maximum degree has list chromatic number at most $(1+o(1))(k-1)\…
Independent sets and colorings of -free graphs
Abhishek Dhawan, Oliver Janzer, Abhishek Methuku
Alon, Krivelevich, and Sudakov conjectured in 1999 that every -free graph of maximum degree at most has chromatic number . This was previously known only for a…
Toward Vu's conjecture
Peter Bradshaw, Abhishek Dhawan, Abhishek Methuku +1
In 2002, Vu conjectured that graphs of maximum degree and maximum codegree at most have chromatic number at most . Despite its importance, the conjecture has re…
Packing subgraphs in regular graphs
Shoham Letzter, Abhishek Methuku, Benny Sudakov
An \emph{-packing} in a graph is a collection of pairwise vertex-disjoint copies of in . We prove that for every and every bipartite graph , any $\lfloor c…
Nearly Hamilton cycles in sublinear expanders, and applications
Shoham Letzter, Abhishek Methuku, Benny Sudakov
We develop novel methods for constructing nearly Hamilton cycles in sublinear expanders with good regularity properties, as well as new techniques for finding such expanders in gen…