5 papers · 1 filter
On -perfect-matching covers of cubic graphs with two adjacent odd circuits in a -factor
Ján Karabáš, Edita Máčajová
Let be a cubic graph admitting a -factor consisting of exactly two odd circuits, and let the complementary -factor contain precisely three spokes (along with an arbitrary…
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…
Regular colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson
Ján Karabáš, Edita Máčajová, 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…
The Jacobian of a graph and graph automorphisms
István Estélyi, Ján Karabáš, Alexander Mednykh +1
In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph in the group of symmetries of the Jacobian of .…
On a representation of the automorphism group of a graph in a unimodular group
István Estelyi, Ján Karabáš, Alexander Mednykh +1
We investigate a representation of the automorphism group of a connected graph in the group of unimodular matrices of dimension , where is the Betti number of grap…