2 citations · 2 across the 5 of their papers we have counts for
6 papers
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…
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 $…
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…
Perfect matching index vs. circular flow number of a cubic graph
Edita Máčajová, Martin Škoviera
The perfect matching index of a cubic graph , denoted by , is the smallest number of perfect matchings that cover all the edges of . According to the Berge-Fulkerson co…
Odd decompositions of eulerian graphs
Edita Máčajová, Martin Škoviera
We prove that an eulerian graph admits a decomposition into closed trails of odd length if and only if and it contains at least pairwise edge-disjoint odd circuits and…