3 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 , let denote the maximum number of neighbors any two distinct vertices of have in common. Vu (2002) proposed that, provided is not too smal…
math.CO2024
Spectral approaches for -improper chromatic number
Krystal Guo, Ross J. Kang, Gabriëlle Zwaneveld
In this paper, we explore algebraic approaches to -improper and -clustered colourings, where the colouring constraints are relaxed to allow some monochromatic edges. Bilu [J.…