Luis Kuffner

collaborators

4 papers

math.CO2026

(Claw, C_3)-free digraphs with unbounded dichromatic number

Guillaume Aubian, Luis Kuffner

We construct orientations of rook graphs (whose underlying graphs are claw-free) that contain no directed $C_{3}$ but have unbounded dichromatic number. This disproves a conjecture o…

math.CO2025

Extension of the GyÃ¡rfÃ¡s-Sumner conjecture to signed graphs

Guillaume Aubian, Allen Ibiapina, Luis Kuffner +4

The balanced chromatic number of a signed graph G is the minimum number of balanced sets that cover all vertices of G. Studying structural conditions which imply bounds on the bala…

math.CO2025

Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs

Luis Kuffner, Reza Naserasr, Lujia Wang +3

The Kneser signed graph $\KS(n,k)$, $k \leq n$ , is the graph whose vertices are signed $k$ -subsets of $[n]$ (i.e. $k$ -subsets $S$ of ${\pm 1, \pm 2, \dots, \pm n}$ such that $S\…

math.CO2025

Fractional balanced chromatic number of signed subcubic graphs

Xiaolan Hu, Luis Kuffner, Jiaao Li +4

A signed graph is a pair $(G, I ¨ )$ , where $G$ is a graph and $I ¨ : E (G) \to {-, +}$ , called signature, is an assignment of signs to the edges. Given a signed graph $(G, I ¨ )$ …