Ross J. Kang

activity

20232026

collaborators

6 papers

math.CO2026

Seymour-tight orientations

Krystal Guo, Ross J. Kang, Gabriëlle Zwaneveld

We investigate `almost counterexamples' to Seymour's second neighbourhood conjecture. In what we call Seymour-tight orientations, the size of the first neighbourhood of each vertex…

math.CO2025

Vu's conjecture holds for claw-free graphs

Linda Cook, Ross J. Kang, Eileen Robinson +1

Given a graph $G$ , let $Δ_{2} (G)$ denote the maximum number of neighbors any two distinct vertices of $G$ have in common. Vu (2002) proposed that, provided $Δ_{2} (G)$ is not too small…

math.CO2025

Triangle-free graphs with the fewest independent sets

Pjotr Buys, Jan van den Heuvel, Ross J. Kang

Given $d > 0$ and a positive integer $n$ , let $G$ be a triangle-free graph on $n$ vertices with average degree $d$ . With an elegant induction, Shearer (1983) tightened a seminal resu…

math.CO2024

Spectral approaches for $d$ -improper chromatic number

Krystal Guo, Ross J. Kang, Gabriëlle Zwaneveld

In this paper, we explore algebraic approaches to $d$ -improper and $t$ -clustered colourings, where the colouring constraints are relaxed to allow some monochromatic edges. Bilu [J.…

math.CO2024

Reconfiguration of Independent Transversals

Pjotr Buys, Ross J. Kang, Kenta Ozeki

Given integers $Δ \geq 2$ and $t \geq 2Δ$ , suppose there is a graph of maximum degree $Δ$ and a partition of its vertices into blocks of size at least $t$ . By a seminal result of Haxel…

math.CO2023

The $χ$ -binding function of $d$ -directional segment graphs

Lech Duraj, Ross J. Kang, Hoang La +4

Given a positive integer $d$ , the class $d$ -DIR is defined as all those intersection graphs formed from a finite collection of line segments in $R^{2}$ having at most $d$ s…