Ronen Wdowinski
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Ronen Wdowinski has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Penny Haxell
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada
2 shared publications - Ross J. Kang
Korteweg-de Vries Institute for Mathematics University of Amsterdam Netherlands
2 shared publications - Stijn Cambie
Department of Computer Science KU Leuven Campus Kulak‐Kortrijk Kortrijk Belgium
2 shared publications Penny Haxell
Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada
1 shared publication
Latest Publications
- Open Access
A precise condition for independent transversals in bipartite covers
Given a bipartite graph $H=(V=V_A\cup V_B,E)$ in which any vertex in $V_A$ (resp.~$V_B$) has degree at most $D_A$ (resp.~$D_B$), suppose there is a partition of $V$ that is a refinement of the bipartition $V_A\cup V_B$ such that the parts in $V_A$ (resp.~$V_B$) have size at least $k_A$ (resp.~$k_B$). We prove that the condition $D_A/k_B+D_B/k_A\le 1$ is sufficient for the existence of an independent set of vertices of $H$ that is simultaneously transversal to the partition, and show moreover that this condition is sharp. This result is a bipartite refinement of two well-known results on independent transversals, one due to the second author and the other due to Szabó and Tardos.Open AccessA precise condition for independent transversals in bipartite covers
Given a bipartite graph $H=(V=V_A\cup V_B,E)$ in which any vertex in $V_A$ (resp.~$V_B$) has degree at most $D_A$ (resp.~$D_B$), suppose there is a partition of $V$ that is a refinement of the bipartition $V_A\cup V_B$ such that the parts in $V_A$ (resp.~$V_B$) have size at least $k_A$ (resp.~$k_B$). We prove that the condition $D_A/k_B+D_B/k_A\le 1$ is sufficient for the existence of an independent set of vertices of $H$ that is simultaneously transversal to the partition, and show moreover that this condition is sharp. This result is a bipartite refinement of two well-known results on independent transversals, one due to the second author and the other due to Szabó and Tardos. - Open Access
- 14 February 2024
- Published by Wiley in Journal of Graph Theory
- Vol. 106 (2) , 352-371
Degree criteria and stability for independent transversals
Anindependent transversal(IT) in a graph with a given vertex partition is an independent set of vertices of (i.e., it induces no edges), that consists of one vertex from each part (block) of . Over the years, various criteria have been established that guarantee the existence of an IT, often given in terms of being ‐thick, meaning all blocks have size at least . One such result, obtained recently by Wanless and Wood, is based on themaximum average block degree. They proved that if then an IT exists. Resolving a problem posed by Groenland, Kaiser, Treffers and Wales (who showed that the ratio 1/4 is best possible), here we give a full characterization of pairs such that the following holds for every : whenever is a graph with maximum degree , and is a ‐thick vertex partition of such that , there exists an IT of with respect to . Our proof makes use of another previously known criterion for the existence of ITs that involve the topological connectedness of the independence complex of graphs, and establishes a general technical theorem on the structure of graphs for which this parameter is bounded above by a known quantity. Our result interpolates between the criterion and the old and frequently applied theorem that if then an IT exists. Using the same approach, we also extend a theorem of Aharoni, Holzman, Howard and Sprüssel, by giving a stability version of the latter result.
- 14 February 2024
- Published by Wiley in Journal of Graph Theory
- Vol. 106 (2) , 352-371
Open AccessDegree criteria and stability for independent transversals
Anindependent transversal(IT) in a graph with a given vertex partition is an independent set of vertices of (i.e., it induces no edges), that consists of one vertex from each part (block) of . Over the years, various criteria have been established that guarantee the existence of an IT, often given in terms of being ‐thick, meaning all blocks have size at least . One such result, obtained recently by Wanless and Wood, is based on themaximum average block degree. They proved that if then an IT exists. Resolving a problem posed by Groenland, Kaiser, Treffers and Wales (who showed that the ratio 1/4 is best possible), here we give a full characterization of pairs such that the following holds for every : whenever is a graph with maximum degree , and is a ‐thick vertex partition of such that , there exists an IT of with respect to . Our proof makes use of another previously known criterion for the existence of ITs that involve the topological connectedness of the independence complex of graphs, and establishes a general technical theorem on the structure of graphs for which this parameter is bounded above by a known quantity. Our result interpolates between the criterion and the old and frequently applied theorem that if then an IT exists. Using the same approach, we also extend a theorem of Aharoni, Holzman, Howard and Sprüssel, by giving a stability version of the latter result.
- 7 November 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 347 (2)
On an f-coloring generalization of linear arboricity of multigraphs
- 7 November 2023
- Published by Elsevier in Discrete Mathematics
- Vol. 347 (2)
On an f-coloring generalization of linear arboricity of multigraphs
- Open Access
- 28 August 2023
- Published by Masaryk University Press in European Conference on Combinatorics, Graph Theory and Applications
- No. 12,p. 263-269
A precise condition for independent transversals in bipartite covers
Given a bipartite graph $H=(V=V_A\cup V_B,E)$ in which any vertex in $V_A$ (resp. $V_B$) has degree at most $D_A$ (resp. $D_B$), suppose there is a partition of $V$ that is a refinement of the bipartition $V_A\cup V_B$ such that the parts in $V_A$ (resp. $V_B$) have size at least $k_A$ (resp. $k_B$). We prove that the condition $D_A/k_A+D_B/k_B\le 1$ is sufficient for the existence of an independent set of vertices of $H$ that is simultaneously transversal to the partition, and show moreover that this condition is sharp.- 28 August 2023
- Published by Masaryk University Press in European Conference on Combinatorics, Graph Theory and Applications
- No. 12,p. 263-269
Open AccessA precise condition for independent transversals in bipartite covers
Given a bipartite graph $H=(V=V_A\cup V_B,E)$ in which any vertex in $V_A$ (resp. $V_B$) has degree at most $D_A$ (resp. $D_B$), suppose there is a partition of $V$ that is a refinement of the bipartition $V_A\cup V_B$ such that the parts in $V_A$ (resp. $V_B$) have size at least $k_A$ (resp. $k_B$). We prove that the condition $D_A/k_A+D_B/k_B\le 1$ is sufficient for the existence of an independent set of vertices of $H$ that is simultaneously transversal to the partition, and show moreover that this condition is sharp. - Open Access
On an $f$-coloring generalization of linear arboricity of multigraphs
Given a multigraph $G$ and function $f : V(G) \rightarrow \mathbb{Z}_{\ge 2}$ on its vertices, a degree-$f$ subgraph of $G$ is a spanning subgraph in which every vertex $v$ has degree at most $f(v)$. The degree-$f$ arboricity $a_f(G)$ of $G$ is the minimum number of colors required to edge-color $G$ into degree-$f$ forests. At least for constant $f$, Truszczyński conjectured that $a_f(G) \le \max \{Δ_f(G) + 1, a(G)\}$ for every multigraph $G$, where $Δ_f(G) = \max_{v \in V(G)} \lceil d(v)/f(v) \rceil$ and $a(G)$ is the usual arboricity of $G$. This is a strong generalization of the Linear Arboricity Conjecture due to Akiyama, Exoo, and Harary. In this paper, we disprove Truszczyński's conjecture in a strong sense for general multigraphs. On the other hand, extending known results for linear arboricity, we prove that the conjecture holds for simple graphs with sufficiently large girth, and that it holds for all simple graphs asymptotically. More strongly, we prove these partial results in the setting of directed graphs, where the color classes are required to be analogously defined degree-$f$ branchings.Open AccessOn an $f$-coloring generalization of linear arboricity of multigraphs
Given a multigraph $G$ and function $f : V(G) \rightarrow \mathbb{Z}_{\ge 2}$ on its vertices, a degree-$f$ subgraph of $G$ is a spanning subgraph in which every vertex $v$ has degree at most $f(v)$. The degree-$f$ arboricity $a_f(G)$ of $G$ is the minimum number of colors required to edge-color $G$ into degree-$f$ forests. At least for constant $f$, Truszczyński conjectured that $a_f(G) \le \max \{Δ_f(G) + 1, a(G)\}$ for every multigraph $G$, where $Δ_f(G) = \max_{v \in V(G)} \lceil d(v)/f(v) \rceil$ and $a(G)$ is the usual arboricity of $G$. This is a strong generalization of the Linear Arboricity Conjecture due to Akiyama, Exoo, and Harary. In this paper, we disprove Truszczyński's conjecture in a strong sense for general multigraphs. On the other hand, extending known results for linear arboricity, we prove that the conjecture holds for simple graphs with sufficiently large girth, and that it holds for all simple graphs asymptotically. More strongly, we prove these partial results in the setting of directed graphs, where the color classes are required to be analogously defined degree-$f$ branchings.