## 708 Citations

### Grid Induced Minor Theorem for Graphs of Small Degree

- MathematicsArXiv
- 2022

A graph H is an induced minor of a graph G if H can be obtained from G by vertex deletions and edge contractions. We show that there is a function f ( k, d ) = O ( k 10 + 2 d 5 ) so that if a graph…

### Obtaining a Planar Graph by Vertex Deletion

- Mathematics, Computer ScienceAlgorithmica
- 2010

A much simpler algorithm for the k-Apex problem with quadratic running time is given, by iteratively reducing the input graph and then applying techniques for graphs of bounded treewidth.

### On the presence of disjoint subgraphs of a specified type

- MathematicsJ. Graph Theory
- 1988

A general sufficient condition for a family of graphs to have the Erdos-Posa property is derived and a polynomially bounded algorithm for finding a cycle of length divisible by m is obtained.

### Induced subgraphs and path decompositions

- Mathematics
- 2022

A graph H is an induced subgraph of a graph G if a graph isomorphic to H can be obtained from G by deleting vertices. Recently, there has been signiﬁcant interest in understanding the unavoidable…

### Packing and covering immersion-expansions of planar sub-cubic graphs

- MathematicsEur. J. Comb.
- 2017

### Shortcutting Planar Digraphs

- MathematicsCombinatorics, Probability and Computing
- 1995

A constructive proof that for any planar digraph G on p vertices, there exists a subset S of the transitive closure of G such that the number of arcs in S is less than or equal to the numberOf arcs in G, and the diameter of G ∪ S is O.

### List-coloring graphs without subdivisions and without immersions

- MathematicsSODA
- 2012

These are the first results concerning list-coloring graphs without fixed graph as a subdivision or as an immersion, except for the known upper bound results and extend the result by Kawarabayashi, Demaine and Hajiaghayi concerning the additive approximation algorithm for list- Colored graphs without Kk as a minor.

### A tight Erdős-Pósa function for planar minors

- MathematicsSODA
- 2019

The present paper proves that for every planar graph $H$ the family of all graphs with a minor isomorphic to $H has the Erdős-Posa property, which is asymptotically best possible for every graph £H with at least one cycle.

### Graph Minors

- Mathematics
- 2009

For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by…

## References

SHOWING 1-10 OF 15 REFERENCES

### Graph Minors. II. Algorithmic Aspects of Tree-Width

- Mathematics, Computer ScienceJ. Algorithms
- 1986

### On Independent Circuits Contained in a Graph

- MathematicsCanadian Journal of Mathematics
- 1965

A family of circuits of a graph G is said to be independent if no two of the circuits have a common vertex; it is called edge-independent if no two of them have an edge in common. A set of vertices…

### From Matrices to Graphs

- MathematicsCanadian Journal of Mathematics
- 1964

All the matrices considered in this paper have their elements in the field of residues mod 2. Two non-singular matrices are equivalent if each row of either matrix is a linear combination of rows of…

### A Hellytype problem in trees , in “ Combinatorial Theory and Its Applications II

- Proc . Colloq . Balatonfured
- 1974