[PDF][PDF] A survey of maximal k-degenerate graphs and k-trees
A Bickle - Theory and Applications of Graphs, 2024 - digitalcommons.georgiasouthern …
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 …
including simple k-trees, k-paths, maximal outerplanar graphs, and Apollonian networks …
Random enriched trees with applications to random graphs
B Stufler - arXiv preprint arXiv:1504.02006, 2015 - arxiv.org
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 …
behaviour of random enriched trees considered up to symmetry. We apply these general …
Limits of random tree-like discrete structures
B Stufler - 2020 - projecteuclid.org
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 …
Adopting this perspective allows us to elegantly prove limits for these structures as instances …
Limits of random tree-like discrete structures
B Stufler - arXiv preprint arXiv:1612.02580, 2016 - arxiv.org
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 …
$\mathcal {R} $-structures and allows for a unified treatment of a large family of random …
Ordered increasing -trees: Introduction and analysis of a preferential attachment network model
A Panholzer, G Seitz - Discrete Mathematics & Theoretical …, 2010 - dmtcs.episciences.org
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 …
a probabilistic preferential attachment rule, but which also has a simple combinatorial …
An Asymptotic Analysis of Labeled and Unlabeled k-Trees
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 …
trees. Our research is motivated by many important algorithmic applications of k-trees in the …
Graph limits of random graphs from a subset of connected k‐trees
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+ …
is uniformly selected from all connected k‐trees of (n+ k) vertices such that the number of (k+ …
The connectivity-profile of random increasing k-trees
A Darrasse, HK Hwang, O Bodini, M Soria - 2010 Proceedings of the Seventh …, 2010 - SIAM
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 …
graphs for which analytic-combinatorial tools can be successfully applied. We study in this …
Shape measures of random increasing k-trees
A Darrasse, HK Hwang, M Soria - Combinatorics, Probability and …, 2016 - cambridge.org
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 …
graphs that have been studied widely, including being used recently as models for complex …
Graph limits of random unlabelled k-trees
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 …
and Gessel (2014) with the cycle-pointing method by Bodirsky, Fusy, Kang and Vigerske …