Related papers: Mapping Class Groups and Interpolating Complexes: …

The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. This latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced…

An interval $k$-graph is the intersection graph of a family $\mathcal{I}$ of intervals of the real line partitioned into at most $k$ classes with vertices adjacent if and only if their corresponding intervals intersect and belong to…

Let ${\cal G}$ be a minor-closed graph class. We say that a graph $G$ is a $k$-apex of ${\cal G}$ if $G$ contains a set $S$ of at most $k$ vertices such that $G\setminus S$ belongs to ${\cal G}$. We denote by ${\cal A}_k ({\cal G})$ the set…

The Ramsey number $R_X(p,q)$ for a class of graphs $X$ is the minimum $n$ such that every graph in $X$ with at least $n$ vertices has either a clique of size $p$ or an independent set of size $q$. We say that Ramsey numbers are linear in…

In this paper we develop a bridge between model theory, geometric topology, and geometric group theory. In particular, we investigate the Ivanov Metaconjecture from the point of view of model theory, and more broadly we seek to answer the…

We continue research into a well-studied family of problems that ask whether the vertices of a graph can be partitioned into sets $A$ and~$B$, where $A$ is an independent set and $B$ induces a graph from some specified graph class ${\cal…

The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of…

Let $x,y\in(0,1]$ and let $A,B,C$ be disjoint nonempty subsets of a graph $G$, where every vertex in $A$ has at least $x|B|$ neighbours in $B$, and every vertex in $B$ has at least $y|C|$ neighbours in $C$. We denote by $\phi(x,y)$ the…

We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height…

We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in…

The main result of the paper is motivated by the following two, apparently unrelated graph optimization problems: (A) as an extension of Edmonds' disjoint branchings theorem, characterize digraphs comprising $k$ disjoint branchings $B_i$…

This work investigates the class of prime star multiplexes, in which each of its layers $i$, $i=1,2, \ldots M$, consists of a regular cycle graph where any node has $2J_i$ neighbors. In a process that does not affect the cyclic topology, it…

Interpreting graph neural networks (GNNs) is difficult because message passing mixes signals and internal channels rarely align with human concepts. We study superposition, the sharing of directions by multiple features, directly in the…

We classify C-groups of ranks $n-1$ and $n-2$ for the symmetric group $S_n$. We also show that all these C-groups correspond to hypertopes, that is, thin, residually connected flag-transitive geometries. Therefore we generalise some similar…

An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…

A paired $k$-to-$k$ disjoint path cover of a graph $G$ is a collection of pairwise disjoint path subgraphs $P_1,P_2,\dotsc,P_k$ such that each $P_i$ has prescribed vertices $s_i$ and $t_i$ as endpoints and the union of $P_1,P_2,\dotsc,P_k$…

A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection. Even though there…

A metrized graph is a compact singular 1-manifold endowed with a metric. A given metrized graph can be modelled by a family of weighted combinatorial graphs. If one chooses a sequence of models from this family such that the vertices become…

We study the class of simple graphs $\mathcal{G}^*$ for which every pair of distinct odd cycles intersect in at most one edge. We give a structural characterization of the graphs in $\mathcal{G}^*$ and prove that every $G \in \mathcal{G}^*$…

An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the minimum number of obstacles over all…