Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Rollin, Jonathan"'
Autor:
Künzel, Benedikt, Rollin, Jonathan
Simultaneous Geometric Embedding (SGE) asks whether, for a given collection of graphs on the same vertex set V, there is an embedding of V in the plane that admits a crossing-free drawing with straightline edges for each of the given graphs. It is kn
Externí odkaz:
http://arxiv.org/abs/2312.09025
A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric arboricity, and he
Externí odkaz:
http://arxiv.org/abs/2302.14721
A graph $F$ is Ramsey for a pair of graphs $(G,H)$ if any red/blue-coloring of the edges of $F$ yields a copy of $G$ with all edges colored red or a copy of $H$ with all edges colored blue. Two pairs of graphs are called Ramsey equivalent if they hav
Externí odkaz:
http://arxiv.org/abs/2206.03898
For a class $\mathcal{D}$ of drawings of loopless (multi-)graphs in the plane, a drawing $D \in \mathcal{D}$ is \emph{saturated} when the addition of any edge to $D$ results in $D' \notin \mathcal{D}$ - this is analogous to saturated graphs in a grap
Externí odkaz:
http://arxiv.org/abs/2012.08631
We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges with endpoints on the vertices of P such that these new edges neither
Externí odkaz:
http://arxiv.org/abs/2008.08413
The interval number of a graph $G$ is the minimum $k$ such that one can assign to each vertex of $G$ a union of $k$ intervals on the real line, such that $G$ is the intersection graph of these sets, i.e., two vertices are adjacent in $G$ if and only
Externí odkaz:
http://arxiv.org/abs/1805.02947
We define the induced arboricity of a graph $G$, denoted by ${\rm ia}(G)$, as the smallest $k$ such that the edges of $G$ can be covered with $k$ induced forests in $G$. This notion generalizes the classical notions of the arboricity and strong chrom
Externí odkaz:
http://arxiv.org/abs/1803.02152
Autor:
Rollin, Jonathan
An ordered graph is a graph equipped with a linear ordering of its vertex set. A pair of ordered graphs is Ramsey finite if it has only finitely many minimal ordered Ramsey graphs and Ramsey infinite otherwise. Here an ordered graph F is an ordered R
Externí odkaz:
http://arxiv.org/abs/1712.09034
Publikováno v:
Journal of Graph Theory; Oct2024, Vol. 106 Issue 4, p741-762, 22p
An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \in \mathbb{Z}^{s \times 4}$, and a vector $\mathbf{p} = (p,\ldots,p) \in \mat
Externí odkaz:
http://arxiv.org/abs/1610.01111