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Cubic graphs with colouring defect 3
Ján Karabáš, Edita Máčajová, Roman Nedela +1
The colouring defect of a cubic graph is the smallest number of edges left uncovered by any set of three perfect matchings. While -edge-colourable graphs have defect , those…
Berge's conjecture for cubic graphs with small colouring defect
Ján Karabáš, Edita Máčajová, Roman Nedela +1
A long-standing conjecture of Berge suggests that every bridgeless cubic graph can be expressed as a union of at most five perfect matchings. This conjecture trivially holds for $3…
Girth, oddness, and colouring defect of snarks
Ján Karabáš, Edita Máčajová, Roman Nedela +1
The colouring defect of a cubic graph, introduced by Steffen in 2015, is the minimum number of edges that are left uncovered by any set of three perfect matchings. Since a cubic gr…