Several min–max relations in graph theory can be expressed in the framework of the Erdős–
Pósa property. Typically, this property reveals a connection between packing and covering …

A chordless cycle, or equivalently a hole, in a graph G is an induced subgraph of G which is
a cycle of length at least 4. We prove that the Erdős-Pósa property holds for chordless …

Let H be a planar graph. By a classical result of Robertson and Seymour, there is a function
f: ℕ→ ℝ such that for all k∊ ℕ and all graphs G, either G contains k vertex-disjoint subgraphs …

An ordered matching of size $ n $ is a graph on a linearly ordered vertex set $ V $, $| V|= 2n
$, consisting of $ n $ pairwise disjoint edges. There are three different ordered matchings of …

We prove that for every graph, any vertex subset S, and given integers: there are k disjoint
cycles of length at least ℓ that each contain at least one vertex from S, or a vertex set of size …

In 1986 Robertson and Seymour proved a generalization of the seminal result of Erd\H {o} s
and P\'osa on the duality of packing and covering cycles: A graph has the Erd\H {o} sP\'osa …

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular,
we suggest two variants of the theorem and we introduce a new, more versatile, concept of …

We prove the existence of a computable function f∶ ℕ→ ℕ such that for every integer k and
every digraph D, either D contains a collection C of k directed cycles of even length such that …

In 1965, Erd\H {o} s and P\'{o} sa proved that there is a duality between the maximum size of
a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality …

We prove that the set of long cycles has the edge-Erdős-Pósa property: for every fixed
integer ℓ≥ 3 and every k∈ ℕ, every graph G either contains k edge-disjoint cycles of length …