Edita Máčajová

activity

20242026

collaborators

5 papers

math.CO2026

On covering cubic graphs with three perfect matchings

Edita MÃ¡ÄajovÃ¡, JÃ¡n MazÃ¡k

For a bridgeless cubic graph $G$ , $m_{3} (G)$ is the ratio of the maximum number of edges of $G$ covered by the union of $3$ perfect matchings to $∣ E (G) ∣$ . We prove that for any $r\in…

math.CO2025

List strong and list normal edge-coloring of (sub)cubic graphs

Borut LuÅ¾ar, Edita MÃ¡ÄajovÃ¡, Roman SotÃ¡k +1

A strong edge-coloring of a graph is a proper edge-coloring, in which the edges of every path of length 3 receive distinct colors; in other words, every pair of edges at distance a…

math.CO2025

Three-cuts are a charm: acyclicity in 3-connected cubic graphs

FrantiÅ¡ek KardoÅ¡, Edita MÃ¡ÄajovÃ¡, Jean Paul Zerafa

Let $G$ be a bridgeless cubic graph. In 2023, the three authors solved a conjecture (also known as the $S_{4}$ -Conjecture) made by Mazzuoccolo in 2013: there exist two perfect matchi…

math.CO2025

Berge's conjecture for cubic graphs with small colouring defect

JÃ¡n KarabÃ¡Å¡, Edita MÃ¡ÄajovÃ¡, Roman Nedela +1

A long-standing conjecture of Berge suggests that every bridgeless cubic graph can be expressed as a union of at most five perfect matchings. This conjecture trivially holds for $3…

math.CO2024

The Frank number and nowhere-zero flows on graphs

Jan Goedgebeur, Edita MÃ¡ÄajovÃ¡, Jarne Renders

An edge $e$ of a graph $G$ is called deletable for some orientation $o$ if the restriction of $o$ to $G - e$ is a strong orientation. Inspired by a problem of Frank, in 2021 HÃ¶rsch…