4 citations · 6 across the 4 of their papers we have counts for
5 papers
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…
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…
Nowhere-zero flows on signed eulerian graphs
Edita Máčajová, Martin Škoviera
This paper is devoted to a detailed study of nowhere-zero flows on signed eulerian graphs. We generalise the well-known fact about the existence of nowhere-zero -flows in euleri…