Robert Šámal

activity

20052026

most citedShort Cycle Covers of Cubic Graphs and Graphs with Minimum Degree Three

22 citations · 60 across the 24 of their papers we have counts for

collaborators

Showing 2017Show all

5 papers · 1 filter

cs.DM2017★ 2 cited

Group Connectivity: $Z_{4}$ v. $Z_{2}^{2}$

Radek Hušek, Lucie Mohelníková, Robert Šámal

We answer a question on group connectivity suggested by Jaeger et al. [Group connectivity of graphs -- A nonhomogeneous analogue of nowhere-zero flow properties, JCTB 1992]: we fin…

math.CO2017

Exponentially many nowhere-zero $Z_{3}$ -, $Z_{4}$ -, and $Z_{6}$ -flows

Zdeněk Dvořák, Bojan Mohar, Robert Šámal

We prove that, in several settings, a graph has exponentially many nowhere-zero flows. These results may be seen as a counting alternative to the well-known proofs of existence of…

math.CO2017

A note on counting flows in signed graphs

Matt DeVos, Edita Rollová, Robert Šámal

Tutte initiated the study of nowhere-zero flows and proved the following fundamental theorem: For every graph $G$ there is a polynomial $f$ so that for every abelian group $Γ$ of o…

math.CO2017

Linear Bound for Majority Colourings of Digraphs

Fiachra Knox, Robert Šámal

Given $η \in [0, 1]$ , a colouring $C$ of $V (G)$ is an $η$ -majority colouring if at most $η d^{+} (v)$ out-neighbours of $v$ have colour $C (v)$ , for any $v \in V (G)$ . We show that every…

math.CO2017★ 1 cited

3-Flows with Large Support

Matt DeVos, Jessica McDonald, Irene Pivotto +2

We prove that every 3-edge-connected graph $G$ has a 3-flow $ϕ$ with the property that $∣ s u pp (ϕ) ∣ \geq \frac{5}{6} ∣ E (G) ∣$ . The graph $K_{4}$ demonstrates that this $\frac{5}…

Group Connectivity: Z4​ v. Z22​

Exponentially many nowhere-zero Z3​-, Z4​-, and Z6​-flows

A note on counting flows in signed graphs

Linear Bound for Majority Colourings of Digraphs

3-Flows with Large Support

Group Connectivity: $Z_{4}$ v. $Z_{2}^{2}$

Exponentially many nowhere-zero $Z_{3}$ -, $Z_{4}$ -, and $Z_{6}$ -flows