Related papers: Regular embeddings of multigraphs

Denote by PSelf(X) (resp., Self(X)) the partial (resp., full) transformation monoid over a set X, and by Sub(V) (resp., End(V)) the collection of all subspaces (resp., endomorphisms) of a vector space V. We prove various results that imply…

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the…

A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold,…

Consider a finite dimensional real vector space and a finite group acting unitarily on it. We study the general problem of constructing Euclidean stable embeddings of the quotient space of orbits. Our embedding is based on subsets of sorted…

In this paper, we introduce a method called graph fusion embedding, designed for multi-graph embedding with shared vertex sets. Under the framework of supervised learning, our method exhibits a remarkable and highly desirable synergistic…

In this paper, we prove that any non-positively curved 2-dimensional surface (alias, Busemann surface) is isometrically embeddable into $L_1$. As a corollary, we obtain that all planar graphs which are 1-skeletons of planar non-positively…

A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, these graphs are studied by presenting some examples and defining some of their sub-structures such as removable…

For a connected reductive group $G_k$ over an algebraically closed field $k$ of char $\neq 2$ and a fixed point subgroup $K_k$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings…

We give an explicit characterization of which direct products $G$ of surface groups of Euclidean type satisfy that the fixed subgroup of any automorphism (or endomorphism) of $G$ is compressed, and of which is it always inert.

We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan…

We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle graph. In particular, we find infinitely many instances of…

We give a new proof for the local existence of a smooth isometric embedding of a smooth $3$-dimensional Riemannian manifold with nonzero Riemannian curvature tensor into $6$-dimensional Euclidean space. Our proof avoids the sophisticated…

We introduce a new class of countably infinite random geometric graphs, whose vertices are points in a metric space, and vertices are adjacent independently with probability p if the metric distance between the vertices is below a given…

Given a natural number k and an orientable surface S of finite type, define the k-curve graph to be the graph with vertices corresponding to isotopy classes of essential simple closed curves on S and with edges corresponding to pairs of…

We prove that, for each circle graph $H$, every graph with sufficiently large rank-width contains a vertex-minor isomorphic to $H$.

Let $G$ be a cubic graph and $\Pi$ be a polyhedral embedding of this graph. The extended graph, $G^{e},$ of $\Pi$ is the graph whose set of vertices is $V(G^{e})=V(G)$ and whose set of edges $E(G^{e})$ is equal to $E(G) \cup \mathcal{S}$,…

Let $\Delta \ge 3$ be fixed, $n \ge n_\Delta$ be a large integer. It is a classical result that $\Delta$--regular expanders on $n$ vertices are not embeddable as geometric (distance) graphs into Euclidean space of dimension less than $c…

Hadwiger's conjecture for the immersion relation posits that every graph $G$ contains an immersion of the complete graph $K_{\chi(G)}$. Vergara showed that this is equivalent to saying that every $n$-vertex graph $G$ with $\alpha(G)=2$…

We study the relationship between the vertices of an up-monotone polyhedron $R$ and those of the polytope $P$ obtained by truncating $R$ with the unit hypercube. When $R$ has binary vertices, we characterize the vertices of $P$ in terms of…

A graph $\Gamma$ is $G$-symmetric if it admits $G$ as a group of automorphisms acting transitively on the set of arcs of $\Gamma$, where an arc is an ordered pair of adjacent vertices. Let $\Gamma$ be a $G$-symmetric graph such that its…