Related papers: Graph-theoretic perspective on a special class of …
Techniques of producing new combinatorial structures from old ones are commonly called trades. The switching principle applies for a broad class of designs: it is a local transformation that modifies two columns of the incidence matrix. In…
A proper vertex coloring of a graph is a mapping of its vertices on a set of colors, such that two adjacent vertices are not mapped to the same color. This constraint may be interpreted in terms of the distance between to vertices and so a…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
We look at colourings of $r$-uniform hypergraphs, focusing our attention on unique colourability and gaps in the chromatic spectrum. The pattern of an edge $E$ in an $r$-uniform hypergraph $H$ whose vertices are coloured is the partition of…
The representation of the resolvent as an integral operator, the $m$ function, and the associated spectral representation are fundamental topics in the spectral theory of self-adjoint ordinary differential operators. Versions of these are…
Let $t\geqslant 2$ and $s\geqslant 1$ be two integers. Define a $(t,s)$-coloring of a hypergraph to be a coloring of its vertices using $t$ colors such that each color appears on each edge at least $s$ times. In this note, we provide a…
In this paper, we initiate the study of discrepancy questions for combinatorial designs. Specifically, we show that, for every fixed $r\ge 3$ and $n\equiv 1,3 \pmod{6}$, any $r$-colouring of the triples on $[n]$ admits a Steiner triple…
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 Heffter array is an m by n matrix with nonzero entries from Z_{2mn+1} such that i) every row and column sum to 0, and ii) no element from {x,-x} appears twice. We construct some Heffter arrays. These arrays are used to build current…
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…
Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…
Higher-rank graphs are, as the name suggests, higher-dimensional analogues of directed graphs which we will define using category theory. The whole idea of my project was to construct what we call a Baumslag-Solitar graph, a higher-rank…
Understanding traffic scenes requires considering heterogeneous information about dynamic agents and the static infrastructure. In this work we propose SCENE, a methodology to encode diverse traffic scenes in heterogeneous graphs and to…
Frei et al. [6] showed that the problem to decide whether a graph is stable with respect to some graph parameter under adding or removing either edges or vertices is $\Theta_2^{\text{P}}$-complete. They studied the common graph parameters…
Hypergraphs offer a generalized framework for understanding complex systems, covering group interactions of different orders beyond traditional pairwise interactions. This modelling allows for the simplified description of simultaneous…
A strict confluent (SC) graph drawing is a drawing of a graph with vertices as points in the plane, where vertex adjacencies are represented not by individual curves but rather by unique smooth paths through a planar system of junctions and…
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…
Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…