## Figures from this paper

## 5 Citations

### A half-integral Erd\H{o}s-P\'osa theorem for directed odd cycles

- Mathematics
- 2020

. We prove that there exists a function f : N → R such that every directed graph G contains either k directed odd cycles where every vertex of G is contained in at most two of them, or a set of at…

### Excluding a Planar Matching Minor in Bipartite Graphs

- MathematicsArXiv
- 2021

A version of Erdős-Pósa property for matching minors is introduced and a direct link between this property and planarity is found and it follows that a class of bipartite graphs with perfect matchings has bounded perfect matching width if and only if it excludes a planar matching minor.

### A relaxation of the Directed Disjoint Paths problem: a global congestion metric helps

- Mathematics, Computer ScienceMFCS
- 2020

## References

SHOWING 1-10 OF 67 REFERENCES

### The Directed Grid Theorem

- MathematicsSTOC
- 2015

The grid theorem is confirmed in full generality to all classes of digraphs excluding a fixed undirected graph as a minor and is able to improve results by Reed 1996 on disjoint cycles of length at least l and by Kawarabayoshi, Kobayashi, Kreutzer on quarter-integral disJoint paths.

### An Excluded Grid Theorem for Digraphs with Forbidden Minors

- MathematicsSODA
- 2014

This paper proves the conjecture that the existence of a function f: N → N such that every digraph of directed tree-width at least f(k) contains a directed grid of order k and proves the excluded grid theorem for the case of digraphs excluding a fixed undirected graph as a minor.

### Polynomial Bounds for the Grid-Minor Theorem

- Mathematics
- 2016

One of the key results in Robertson and Seymour’s seminal work on graph minors is the grid-minor theorem (also called the excluded grid theorem). The theorem states that for every grid H, every graph…

### Excluding A Grid Minor In Planar Digraphs

- MathematicsArXiv
- 2015

The conjecture that a digraph of huge tree-width has a large "cylindrical grid" minor is proved, not only for planar digraphs, but many steps of the proof work in general.

### Complexity of finding embeddings in a k -tree

- Mathematics, Computer Science
- 1987

This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.

### An algorithmic metatheorem for directed treewidth

- Mathematics, Computer ScienceDiscret. Appl. Math.
- 2016

### The Erdos-Posa Property for Directed Graphs

- MathematicsArXiv
- 2016

A complete characterisation of the class of strongly connected digraphs which have the Erd˝ os-Posa-property is obtained (both for topological and butterfly minors) and this result is generalised to classes of dig graphs which are not strongly connected.

### Towards a Polynomial Kernel for Directed Feedback Vertex Set

- Mathematics, Computer ScienceMFCS
- 2017

Two main contributions are provided: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.

### Digraph decompositions and monotonicity in digraph searching

- Computer ScienceTheor. Comput. Sci.
- 2011