D. Rautenbach

activity

20092023

most citedHow to determine if a random graph with a fixed degree sequence has a giant component

18 citations · 46 across the 68 of their papers we have counts for

collaborators

Showing 2016Show all

10 papers · 1 filter

math.CO2016★ 1 cited

Uniquely restricted matchings and edge colorings

Julien Baste, Dieter Rautenbach, Ignasi Sau

A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. This notion was defined by Golumbic, Hirst, and Lewenstein and studied in…

math.CO2016

Large Values of the Clustering Coefficient

Michael Gentner, Irene Heinrich, Simon Jäger +1

A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature 393 (1998) 440-442), is t…

math.CO2016

Extremal Values of the Chromatic Number for a Given Degree Sequence

Stéphane Bessy, Dieter Rautenbach

For a degree sequence $d : d_{1} \geq \dots \geq d_{n}$ , we consider the smallest chromatic number $χ_{m i n} (d)$ and the largest chromatic number $χ_{m a x} (d)$ among all graphs with degr…

math.CO2016

Some Comments on the Slater number

Michael Gentner, Dieter Rautenbach

Let $G$ be a graph with degree sequence $d_{1} \geq \dots \geq d_{n}$ . Slater proposed $s ℓ (G) = min {s : (d_{1} + 1) + \dots + (d_{s} + 1) \geq n}$ as a lower bound on the domination number $γ(…

math.CO2016

Some Bounds on the Zero Forcing Number of a Graph

Michael Gentner, Dieter Rautenbach

A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$ , and then, iterative…

math.CO2016

Exponential Independence

Simon Jäger, Dieter Rautenbach

For a set $S$ of vertices of a graph $G$ , a vertex $u$ in $V (G) ∖ S$ , and a vertex $v$ in $S$ , let $dist_{(G, S)} (u, v)$ be the distance of $u$ and $v$ in the graph $G-(…