Ross J. Kang

activity

20242026

collaborators

4 papers

math.CO2026

Seymour-tight orientations

Krystal Guo, Ross J. Kang, GabriÃ«lle 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 $I^_{2} (G)$ denote the maximum number of neighbors any two distinct vertices of $G$ have in common. Vu (2002) proposed that, provided $I^_{2} (G)$ is not too smal…

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, GabriÃ«lle 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.…

Seymour-tight orientations

Vu's conjecture holds for claw-free graphs

Triangle-free graphs with the fewest independent sets

Spectral approaches for d-improper chromatic number

Spectral approaches for $d$ -improper chromatic number