This article surveys results on maximal k-degenerate graphs, k-trees, and related classes
including simple k-trees, k-paths, maximal outerplanar graphs, and Apollonian networks …

We establish limit theorems that describe the asymptotic local and global geometric
behaviour of random enriched trees considered up to symmetry. We apply these general …

Many random recursive discrete structures may be described by a single generic model.
Adopting this perspective allows us to elegantly prove limits for these structures as instances …

We study a model of random $\mathcal {R} $-enriched trees that is based on weights on the
$\mathcal {R} $-structures and allows for a unified treatment of a large family of random …

We introduce a random graph model based on k-trees, which can be generated by applying
a probabilistic preferential attachment rule, but which also has a simple combinatorial …

In this paper we provide a systematic treatment of several shape parameters of (random) k-
trees. Our research is motivated by many important algorithmic applications of k-trees in the …

For any set Ω of non‐negative integers such that, we consider a random Ω‐k‐tree G n, k that
is uniformly selected from all connected k‐trees of (n+ k) vertices such that the number of (k+ …

Random increasing k-trees represent an interesting, useful class of strongly dependent
graphs for which analytic-combinatorial tools can be successfully applied. We study in this …

Random increasing k-trees represent an interesting and useful class of strongly dependent
graphs that have been studied widely, including being used recently as models for complex …

We study random unlabelled k-trees by combining the colouring approach by Gainer-Dewar
and Gessel (2014) with the cycle-pointing method by Bodirsky, Fusy, Kang and Vigerske …