Related papers: Structure and enumeration theorems for hereditary …
Starting from a succession rule for Catalan numbers, we define a procedure encoding and listing the objects enumerated by these numbers such that two consecutive codes of the list differ only for one digit. Gray code we obtain can be…
Structural convergence is a framework for convergence of graphs by Ne\v{s}et\v{r}il and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given…
Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ${\cal P}$ and those that are far from satisfying it. Since these algorithms operate by inspecting a small…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Hereditarily finite sets (sets which are finite and have only hereditarily finite sets as members) are basic mathematical and computational objects, and also stand at the basis of some programming languages. This raises the need for…
It is known that context-free grammars can be extended to generating graphs resulting in graph grammars; one of such fundamental approaches is hyperedge replacement grammars. On the other hand there are type-logical grammars which also…
Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…
End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can topologically be represented by a…
We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer…
A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…
Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems. We formulate…
One of the most fundamental questions in graph property testing is to characterize the combinatorial structure of properties that are testable with a constant number of queries. We work towards an answer to this question for the…
A class ${\cal F}$ of graphs is called {\em tame} if there exists a constant $k$ so that every graph in ${\cal F}$ on $n$ vertices contains at most $O(n^k)$ minimal separators, {\em strongly-quasi-tame} if every graph in ${\cal F}$ on $n$…
A relational structure R is ultrahomogeneous if every isomorphism of finite induced substructures of R extends to an automorphism of R. We classify the ultrahomogeneous finite binary relational structures with one asymmetric binary relation…
A graph $G$ is $\textit{universal}$ for a (finite) family $\mathcal{H}$ of graphs if every $H \in \mathcal{H}$ is a subgraph of $G$. For a given family $\mathcal{H}$, the goal is to determine the smallest number of edges an…
We study Extremal Combinatorics problems where local properties are used to derive global properties. That is, we consider a given configuration where every small piece of the configuration satisfies some restriction, and use this local…
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Asymptotic properties of finitely generated subgroups of free groups, and of finite group presentations, can be considered in several fashions, depending on the way these objects are represented and on the distribution assumed on these…