Add to ORKGWe show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mariño
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce ...
This article proves the conjecture of Thomas that, for every graph G, there is an integer k such tha...
AbstractThis article proves the conjecture of Thomas that, for every graph G, there is an integer k ...
International audienceWe show that a small tree-decomposition of a knot diagram induces a small sphe...
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When...
ABSTRACT. We consider compact 3-manifolds M having a submersion h to R in which each generic point i...
We characterize all graphs that have carving-width at most k for k=1,2,3. In particular, we show th...
We define the Wirtinger width of a knot. Then we prove the Wirtinger width of a knot equals its Gaba...
The tree-width and branch-width of a graph are two well-studied examples of parameters that measure ...
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a questio...
For their famous algorithm for the disjoint paths problem, Robertson and Seymour proved that there i...
International audienceIn Graph Minor III, Robertson and Seymour conjecture that the difference betwe...
Abstract. Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to constr...
A hole in a graph is a chordless cycle of length at least four. A graph is even-hole-free if it does...
Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph G ...
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce ...
This article proves the conjecture of Thomas that, for every graph G, there is an integer k such tha...
AbstractThis article proves the conjecture of Thomas that, for every graph G, there is an integer k ...
International audienceWe show that a small tree-decomposition of a knot diagram induces a small sphe...
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When...
ABSTRACT. We consider compact 3-manifolds M having a submersion h to R in which each generic point i...
We characterize all graphs that have carving-width at most k for k=1,2,3. In particular, we show th...
We define the Wirtinger width of a knot. Then we prove the Wirtinger width of a knot equals its Gaba...
The tree-width and branch-width of a graph are two well-studied examples of parameters that measure ...
If X is a collection of edges in a graph G, let G/X denote the contraction of X. Following a questio...
For their famous algorithm for the disjoint paths problem, Robertson and Seymour proved that there i...
International audienceIn Graph Minor III, Robertson and Seymour conjecture that the difference betwe...
Abstract. Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to constr...
A hole in a graph is a chordless cycle of length at least four. A graph is even-hole-free if it does...
Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph G ...
In this paper we discuss the applications of knotoids to modelling knots in open curves and produce ...
This article proves the conjecture of Thomas that, for every graph G, there is an integer k such tha...
AbstractThis article proves the conjecture of Thomas that, for every graph G, there is an integer k ...