Anita Liebenau
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Anita Liebenau has a total of 63 co-authors. Here are the top co-authors by number of shared publications:
Dennis Clemens
4 shared publications- Dennis Clemens
Department of Mathematics and Computer Science Freie Universität Berlin Germany
4 shared publications - Dennis Clemens
Tech Univ Hamburg, Inst Math, Schwarzenberg Campus 3, D-21073 Hamburg, Germany
4 shared publications - Natasha Morrison
Department of Mathematics and Statistics University of Victoria
4 shared publications - Nina Kamčev
Department of Mathematics, Faculty of Science, University of Zagreb, Zagreb, Croatia
4 shared publications - Asaf Ferber
School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences Tel Aviv University 69978 Tel Aviv Israel
3 shared publications
Latest Publications
- Open Access
- 11 March 2026
- Published by Wiley in Random Structures & Algorithms
- Vol. 68 (2) , e70055
Universality for Graphs of Bounded Degeneracy
- 11 March 2026
- Published by Wiley in Random Structures & Algorithms
- Vol. 68 (2) , e70055
Open AccessUniversality for Graphs of Bounded Degeneracy
- 3 July 2025
- Published by Springer Nature
- p. 711-716
A New Family of Sidorenko Linear Configurations
- Open Access
An Improved Upper Bound on the Threshold Bias of the Oriented-cycle game
We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by OBreaker directing between one and $b$ previously undirected edges. The game ends once all edges have been directed, and OMaker wins if and only if the resulting tournament contains a directed cycle. Bollobás and Szabó asked the following question: what is the largest value of the bias $b$ for which OMaker has a winning strategy? Ben-Eliezer, Krivelevich and Sudakov proved that OMaker has a winning strategy for $b \leq n/2 - 2$. In the other direction, Clemens and Liebenau proved that OBreaker has a winning strategy for $b \geq 5n/6+2$. Inspired by their approach, we propose a significantly stronger strategy for OBreaker which we prove to be winning for $b \geq 0.7845n + O(1)$.Open AccessAn Improved Upper Bound on the Threshold Bias of the Oriented-cycle game
We study the $b$-biased Oriented-cycle game where two players, OMaker and OBreaker, take turns directing the edges of $K_n$ (the complete graph on $n$ vertices). In each round, OMaker directs one previously undirected edge followed by OBreaker directing between one and $b$ previously undirected edges. The game ends once all edges have been directed, and OMaker wins if and only if the resulting tournament contains a directed cycle. Bollobás and Szabó asked the following question: what is the largest value of the bias $b$ for which OMaker has a winning strategy? Ben-Eliezer, Krivelevich and Sudakov proved that OMaker has a winning strategy for $b \leq n/2 - 2$. In the other direction, Clemens and Liebenau proved that OBreaker has a winning strategy for $b \geq 5n/6+2$. Inspired by their approach, we propose a significantly stronger strategy for OBreaker which we prove to be winning for $b \geq 0.7845n + O(1)$. - 26 August 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 38 (3) , 2297-2311
On Multicolor Turán Numbers
We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let [Formula: see text] be a fixed graph and let [Formula: see text] be the union of [Formula: see text] edge-disjoint copies of [Formula: see text], namely [Formula: see text], where each [Formula: see text] is isomorphic to a fixed graph [Formula: see text] and [Formula: see text] for all [Formula: see text]. We call a subgraph [Formula: see text] multicolored if [Formula: see text] and [Formula: see text] share at most one edge for all [Formula: see text]. Define [Formula: see text] to be the maximum value [Formula: see text] such that there exists [Formula: see text] on [Formula: see text] vertices without a multicolored copy of [Formula: see text]. We show that [Formula: see text] and that all extremal graphs are close to a blow-up of the 5-cycle. This bound is tight up to the linear error term.
- 26 August 2024
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 38 (3) , 2297-2311
On Multicolor Turán Numbers
We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let [Formula: see text] be a fixed graph and let [Formula: see text] be the union of [Formula: see text] edge-disjoint copies of [Formula: see text], namely [Formula: see text], where each [Formula: see text] is isomorphic to a fixed graph [Formula: see text] and [Formula: see text] for all [Formula: see text]. We call a subgraph [Formula: see text] multicolored if [Formula: see text] and [Formula: see text] share at most one edge for all [Formula: see text]. Define [Formula: see text] to be the maximum value [Formula: see text] such that there exists [Formula: see text] on [Formula: see text] vertices without a multicolored copy of [Formula: see text]. We show that [Formula: see text] and that all extremal graphs are close to a blow-up of the 5-cycle. This bound is tight up to the linear error term.
- Open Access
- 4 August 2024
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 264 (1) , 331-362
On uncommon systems of equations
A linear system L over $$\mathbb{F}_{q}$$ is common if the number of monochromatic solutions to L = 0 in any two-colouring of $$\mathbb{F}_{q}^{n}$$ is asymptotically at least the expected number of monochromatic solutions in a random two-colouring of $$\mathbb{F}_{q}^{n}$$ . Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions), as well as extensive research on common and Sidorenko graphs, Saad and Wolf recently initiated the systematic study of common systems of linear equations.Building upon earlier work of Cameron, Cilleruelo and Serra, as well as Saad and Wolf, common linear equations have recently been fully characterised by Fox, Pham and Zhao, who asked about common systems of equations. In this paper we move towards a classification of common systems of two or more linear equations. In particular we prove that any system containing an arithmetic progression of length four is uncommon, resolving a question of Saad and Wolf. This follows from a more general result which allows us to deduce the uncommonness of a general system from certain properties of one- or two-equation subsystems.- 4 August 2024
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 264 (1) , 331-362
Open AccessOn uncommon systems of equations
A linear system L over $$\mathbb{F}_{q}$$ is common if the number of monochromatic solutions to L = 0 in any two-colouring of $$\mathbb{F}_{q}^{n}$$ is asymptotically at least the expected number of monochromatic solutions in a random two-colouring of $$\mathbb{F}_{q}^{n}$$ . Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions), as well as extensive research on common and Sidorenko graphs, Saad and Wolf recently initiated the systematic study of common systems of linear equations.Building upon earlier work of Cameron, Cilleruelo and Serra, as well as Saad and Wolf, common linear equations have recently been fully characterised by Fox, Pham and Zhao, who asked about common systems of equations. In this paper we move towards a classification of common systems of two or more linear equations. In particular we prove that any system containing an arithmetic progression of length four is uncommon, resolving a question of Saad and Wolf. This follows from a more general result which allows us to deduce the uncommonness of a general system from certain properties of one- or two-equation subsystems. - Open Access
On the uncommonness of minimal rank-2 systems of linear equations
We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kamčev, Morrison and the second author. Moreover, we prove that any large system containing such a $(2\times k)$-system as a minimal subsystem is uncommon.
Open AccessOn the uncommonness of minimal rank-2 systems of linear equations
We prove that suitably generic pairs of linear equations on an even number of variables are uncommon. This verifies a conjecture of Kamčev, Morrison and the second author. Moreover, we prove that any large system containing such a $(2\times k)$-system as a minimal subsystem is uncommon.
- Open Access
Towards a characterisation of Sidorenko systems
A system of linear forms $L=\{L_1,\ldots,L_m\}$ over $\mathbb{F}_q$ is said to be Sidorenko if the number of solutions to $L=0$ in any $A \subseteq \mathbb{F}_{q}^n$ is asymptotically as $n\to\infty$ at least the expected number of solutions in a random set of the same density. Work of Saad and Wolf (2017) and of Fox, Pham and Zhao (2019) fully characterises single equations with this property and both sets of authors ask about a characterisation of Sidorenko systems of equations. In this paper, we make progress towards this goal. Firstly, we find a simple necessary condition for a system to be Sidorenko, thus providing a rich family of non-Sidorenko systems. In the opposite direction, we find a large family of structured Sidorenko systems, by utilising the entropy method. We also make significant progress towards a full classification of systems of two equations.Open AccessTowards a characterisation of Sidorenko systems
A system of linear forms $L=\{L_1,\ldots,L_m\}$ over $\mathbb{F}_q$ is said to be Sidorenko if the number of solutions to $L=0$ in any $A \subseteq \mathbb{F}_{q}^n$ is asymptotically as $n\to\infty$ at least the expected number of solutions in a random set of the same density. Work of Saad and Wolf (2017) and of Fox, Pham and Zhao (2019) fully characterises single equations with this property and both sets of authors ask about a characterisation of Sidorenko systems of equations. In this paper, we make progress towards this goal. Firstly, we find a simple necessary condition for a system to be Sidorenko, thus providing a rich family of non-Sidorenko systems. In the opposite direction, we find a large family of structured Sidorenko systems, by utilising the entropy method. We also make significant progress towards a full classification of systems of two equations. - 23 March 2023
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mathematics
- Vol. 74 (3) , 957-974
Towards a characterization of Sidorenko systems
A system of linear forms |$L=\{L_1,\ldots,L_m\}$| over |$\mathbb{F}_q$| is said to be Sidorenko if the number of solutions to L = 0 in any |$A \subseteq \mathbb{F}_{q}^n$| is asymptotically as |$n\to\infty$| at least the expected number of solutions in a random set of the same density. Work of Saad and Wolf [19] and of Fox, Pham and Zhao [8] fully characterizes single equations with this property and both sets of authors ask about a characterization of Sidorenko systems of equations. In this paper, we make progress towards this goal. First, we find a simple necessary condition for a system to be Sidorenko, thus providing a rich family of non-Sidorenko systems. In the opposite direction, we find a large family of structured Sidorenko systems, by utilizing the entropy method. We also make significant progress towards a full classification of systems of two equations.
- 23 March 2023
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mathematics
- Vol. 74 (3) , 957-974
Towards a characterization of Sidorenko systems
A system of linear forms |$L=\{L_1,\ldots,L_m\}$| over |$\mathbb{F}_q$| is said to be Sidorenko if the number of solutions to L = 0 in any |$A \subseteq \mathbb{F}_{q}^n$| is asymptotically as |$n\to\infty$| at least the expected number of solutions in a random set of the same density. Work of Saad and Wolf [19] and of Fox, Pham and Zhao [8] fully characterizes single equations with this property and both sets of authors ask about a characterization of Sidorenko systems of equations. In this paper, we make progress towards this goal. First, we find a simple necessary condition for a system to be Sidorenko, thus providing a rich family of non-Sidorenko systems. In the opposite direction, we find a large family of structured Sidorenko systems, by utilizing the entropy method. We also make significant progress towards a full classification of systems of two equations.
- 20 January 2023
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 37 (1) , 25-50
On the Minimum Degree of Minimal Ramsey Graphs for Cliques Versus Cycles
A graph \(G\) is said to be \(q\) -Ramsey for a \(q\) -tuple of graphs \((H_1,\ldots,H_q)\) , denoted by \(G\to_q(H_1,\ldots,H_q)\) , if every \(q\) -edge-coloring of \(G\) contains a mon...- 20 January 2023
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 37 (1) , 25-50
On the Minimum Degree of Minimal Ramsey Graphs for Cliques Versus Cycles
A graph \(G\) is said to be \(q\) -Ramsey for a \(q\) -tuple of graphs \((H_1,\ldots,H_q)\) , denoted by \(G\to_q(H_1,\ldots,H_q)\) , if every \(q\) -edge-coloring of \(G\) contains a mon...- Open Access
On uncommon systems of equations
A system of linear equations $L$ over $\mathbb{F}_q$ is common if the number of monochromatic solutions to $L$ in any two-colouring of $\mathbb{F}_q^n$ is asymptotically at least the expected number of monochromatic solutions in a random two-colouring of $\mathbb{F}_q^n$. Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions), as well as extensive research on common and Sidorenko graphs, the systematic study of common systems of linear equations was recently initiated by Saad and Wolf. Building upon earlier work of Cameron, Cilleruelo and Serra, as well as Saad and Wolf, common linear equations have recently been fully characterised by Fox, Pham and Zhao, who asked about common \emph{systems} of equations. In this paper we move towards a classification of common systems of two or more linear equations. In particular we prove that any system containing an arithmetic progression of length four is uncommon, confirming a conjecture of Saad and Wolf. This follows from a more general result which allows us to deduce the uncommonness of a general system from certain properties of one- or two-equation subsystems.Open AccessOn uncommon systems of equations
A system of linear equations $L$ over $\mathbb{F}_q$ is common if the number of monochromatic solutions to $L$ in any two-colouring of $\mathbb{F}_q^n$ is asymptotically at least the expected number of monochromatic solutions in a random two-colouring of $\mathbb{F}_q^n$. Motivated by existing results for specific systems (such as Schur triples and arithmetic progressions), as well as extensive research on common and Sidorenko graphs, the systematic study of common systems of linear equations was recently initiated by Saad and Wolf. Building upon earlier work of Cameron, Cilleruelo and Serra, as well as Saad and Wolf, common linear equations have recently been fully characterised by Fox, Pham and Zhao, who asked about common \emph{systems} of equations. In this paper we move towards a classification of common systems of two or more linear equations. In particular we prove that any system containing an arithmetic progression of length four is uncommon, confirming a conjecture of Saad and Wolf. This follows from a more general result which allows us to deduce the uncommonness of a general system from certain properties of one- or two-equation subsystems.