Roman Nedela

collaborators

2 papers

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…