3 papers
math.CO2026
A Linear Bound on the Rich Flow Number for Graphs with a Given Maximum Degree
Robert Lukoťka
A rich -flow is a nowhere-zero -flow such that, for every pair of adjacent edges and , . A graph is rich flow admissible if it admits a rich $k…
math.CO2025
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 $…
math.CO2015
Short cycle covers on cubic graphs using chosen 2-factor
Barbora Candráková, Robert Lukoťka
We show that every bridgeless cubic graph with edges has a cycle cover of length at most . Moreover, if does not contain any intersecting circuits of length ,…