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math.CO2022★ 1 cited
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…
math.CO2022★ 7 cited
Disjoint odd circuits in a bridgeless cubic graph can be quelled by a single perfect matching
František Kardoš, Edita Máčajová, Jean Paul Zerafa
Let be a bridgeless cubic graph. The Berge--Fulkerson Conjecture (1970s) states that admits a list of six perfect matchings such that each edge of belongs to exactly tw…