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Random independent sets in uncrowded hypergraphs
Abhishek Dhawan, Lina Li, Abhishek Methuku +2
Given any fixed integer and sufficiently large , we show that the largest possible fractional chromatic number of a -uniform -degenerate uncrowded hypergraph …
Fractional DP-colorings of -degenerate locally sparse graphs
Abhishek Dhawan, Huy Nguyen, Rohan A. Rathi
Bernshteyn, Kostochka, and Zhu (2020) introduced the notion of fractional DP-coloring, which generalizes both fractional coloring and fractional list coloring. Among several founda…
Sharp bounds for the fractional chromatic number of high-girth -degenerate graphs
Peter Allen, Abhishek Dhawan, Jonathan A. Noel
Martinsson and Steiner recently proved that the fractional chromatic number of any -degenerate triangle-free graph satisfies . They…
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)\…
Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs
Abhishek Dhawan, Nhi U. Dinh, Eren C. Kızıldağ +2
We study the algorithmic tractability of finding large independent sets in dense random hypergraphs. In the sparse regime, much of the natural algorithms can be formulated within e…
The strong chromatic index of -free graphs
Richard Bi, Peter Bradshaw, Abhishek Dhawan +1
A strong edge coloring of a graph is an edge coloring such that each color class forms an induced matching in . The strong chromatic index…
Fractional coloring via entropy
Abhishek Dhawan
In recent work, Martinsson and Steiner proved that triangle-free -degenerate graphs have fractional chromatic number . Here, we introduc…