J'an Karab'avs

collaborators

3 papers

math.CO2026

On $4$ -covers of cubic graphs with two adjacent odd circuits in a $2$ -factor

JÃ¡n KarabÃ¡Å¡, Edita MÃ¡ÄajovÃ¡

Let $G$ be a cubic graph admitting a $2$ -factor consisting of exactly two odd circuits, and let the complementary $1$ -factor contain precisely three spokes (along with an arbitrary…

math.CO2025

Cubic graphs of colouring defect 3 and conjectures of Berge and Alon-Tarsi

JÃ¡n KarabÃ¡Å¡, Edita MÃ¡ÄajovÃ¡, Roman Nedela +1

We study two measures of uncolourability of cubic graphs, their colouring defect and perfect matching index. The colouring defect of a cubic graph $G$ is the smallest number of edg…

math.CO2025

Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson

JÃ¡n KarabÃ¡Å¡, Edita MÃ¡ÄajovÃ¡, Roman Nedela +1

We introduce a new invariant of a cubic graph - its regular colouring defect - which is defined as the smallest number of edges left uncovered by any collection of three perfect ma…

On 4-covers of cubic graphs with two adjacent odd circuits in a 2-factor

Cubic graphs of colouring defect 3 and conjectures of Berge and Alon-Tarsi

Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson

On $4$ -covers of cubic graphs with two adjacent odd circuits in a $2$ -factor