2 citations · 2 across the 2 of their papers we have counts for
6 papers
Decomposition of cubic graphs with cyclic connectivity 5
Edita Máčajová, Jozef Rajník
Let be a cyclically -connected cubic graph with a -edge-cut separating into two cyclic components and . We prove that each component can be completed…
Cubic graphs that cannot be covered with four perfect matchings
Edita Máčajová, Martin Škoviera
A conjecture of Berge suggests that every bridgeless cubic graph can have its edges covered with at most five perfect matchings. Since three perfect matchings suffice only when the…
The smallest nontrivial snarks of oddness 4
Jan Goedgebeur, Edita Máčajová, Martin Škoviera
The oddness of a cubic graph is the smallest number of odd circuits in a 2-factor of the graph. This invariant is widely considered to be one of the most important measures of unco…
Critical and flow-critical snarks coincide
Edita Máčajová, Martin Škoviera
Over the past twenty years, critical and bicritical snarks have been appearing in the literature in various forms and in different contexts. Two main variants of criticality of sna…
Shorter signed circuit covers of graphs
Tomáš Kaiser, Robert Lukot'ka, Edita Máčajová +1
A signed circuit is a minimal signed graph (with respect to inclusion) that admits a nowhere-zero flow. We show that each flow-admissible signed graph on edges can be covered b…
Small snarks with large oddness
Robert Lukotka, Edita Macajova, Jan Mazak +1
We estimate the minimum number of vertices of a cubic graph with given oddness and cyclic connectivity. We prove that a bridgeless cubic graph with oddness other than th…