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math.CO2025
Cubic graphs of colouring defect 3 and conjectures of Berge and Alon-Tarsi
Ján Karabáš, Edita Máčajová, 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 is the smallest number of edg…
math.CO2025
Cages and cyclic connectivity
Robert Lukoťka, Edita Máčajová, Jozef Rajník
A graph is cyclically -edge-connected if there is no set of fewer than edges that disconnects into at least two cyclic components. We prove that if a -cage $…