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- Henning Bruhn, Maya Jakobine Stein
- J. Comb. Theory, Ser. B
- 2006

MacLaneâ€™s planarity criterion states that a finite graph is planar if and only if its cycle space has a basis B such that every edge is contained in at most two members of B. Solving a problem ofâ€¦ (More)

- Maya Jakobine Stein
- Discrete Mathematics
- 2011

We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problemsâ€¦ (More)

- Henning Bruhn, Maya Jakobine Stein
- Combinatorica
- 2007

We introduce a natural extension of the vertex degree to ends. For the cycle space C(G) as proposed by Diestel and KÃ¼hn [4, 5], which allows for infinite cycles, we prove that the edge set of aâ€¦ (More)

- Henning Bruhn, Reinhard Diestel, Maya Jakobine Stein
- Journal of Graph Theory
- 2005

A well-known conjecture of ErdÅ‘s states that, given an infinite graph G and sets A,B âŠ† V (G), there exists a family of disjoint Aâ€“B paths P together with an Aâ€“B separator X consisting of a choice ofâ€¦ (More)

- Henning Bruhn, Maya Jakobine Stein
- Math. Program.
- 2012

A graph is called t-perfect, if its stable set polytope is defined by nonnegativity, edge and odd-cycle inequalities. We characterise the class of all claw-free t-perfect graphs by forbiddenâ€¦ (More)

- Johannes Carmesin, Reinhard Diestel, Fabian Hundertmark, Maya Jakobine Stein
- Combinatorica
- 2014

Considering systems of separations in a graph that separate every pair of a given set of vertex sets that are themselves not separated by these separations, we determine conditions under which such aâ€¦ (More)

- Maya Jakobine Stein
- Journal of Graph Theory
- 2007

By a theorem of Mader [5], highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. Solving a problem of Diestel [2], we extend this result to infinite graphs.â€¦ (More)

It is well-known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, weâ€¦ (More)

- Henning Bruhn, Reinhard Diestel, Maya Jakobine Stein
- Journal of Graph Theory
- 2005

By a result of Gallai, every finite graph G has a vertex partition into two parts each inducing an element of its cycle space. This fails for infinite graphs if, as usual, the cycle space is definedâ€¦ (More)

- Maya Jakobine Stein
- J. Comb. Theory, Ser. B
- 2006

Nash-Williamsâ€™ arboricity theorem states that a finite graph is the edge-disjoint union of at most k forests if no set of ` vertices induces more than k(`âˆ’ 1) edges. We prove a natural topologicalâ€¦ (More)