Related papers: L-Graphs and Monotone L-Graphs
A book embedding of a complete graph is a spatial embedding whose planar projection has the vertices located along a circle, consecutive vertices are connected by arcs of the circle, and the projections of the remaining "interior" edges in…
We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two…
An ordinary voltage graph embedding of a graph in a surface encodes a certain kind of highly symmetric covering space of that surface. Given an ordinary voltage graph embedding of a graph $G$ in a surface with voltage group $A$ and a…
Graph embedding techniques are pivotal in real-world machine learning tasks that operate on graph-structured data, such as social recommendation and protein structure modeling. Embeddings are mostly performed on the node level for learning…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Extending Stallings' foldings of trees, we show in this article that every parallel-preserving map between median graphs factors as an isometric embedding through a sequence of elementary transformations which we call foldings and…
Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. In this paper we provide several novel characterizations of planar median…
We prove the following variant of Levi's Enlargement Lemma: for an arbitrary arrangement $\mathcal{A}$ of $x$-monotone pseudosegments in the plane and a pair of points $a,b$ with distinct $x$-coordinates and not on the same pseudosegment,…
An edge-ordered graph is a graph with a total ordering of its edges. A path $P=v_1v_2\ldots v_k$ in an edge-ordered graph is called increasing if $(v_iv_{i+1}) > (v_{i+1}v_{i+2})$ for all $i = 1,\ldots,k-2$; it is called decreasing if…
A graph G is weakly 4-connected if it is 3-connected, has at least five vertices, and for every pair of sets (A,B) with union V(G) and intersection of size three such that no edge has one end in A-B and the other in B-A, one of the induced…
Graph embedding is a transformation of vertices of a graph into set of vectors. Good embeddings should capture the graph topology, vertex-to-vertex relationship, and other relevant information about graphs, subgraphs, and vertices. If these…
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers. This includes freely jointed chains, steric effects,…
A relational structure is homomorphism-homogeneous (HH-homogeneous for short) if every homomorphism between finite induced substructures of the structure can be extended to a homomorphism over the whole domain of the structure. Similarly, a…
A rectangle visibility representation (RVR) of a graph consists of an assignment of axis-aligned rectangles to vertices such that for every edge there exists a horizontal or vertical line of sight between the rectangles assigned to its…
If we parameterize the positions of all vertices of a given graph in the plane such that distances between adjacent vertices are fixed, we obtain a moving graph. An L-linkage is a realization of a moving graph in 3D-space, by representing…
An embedding of a graph on a translation surface is said to be \emph{systolic} if each vertex of the graph corresponds to a singular point (or marked point) and each edge corresponds to a shortest saddle connection on the translation…
In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersection. This is not true in general and various counterexamples have been found. However, the answer to Gallai's question is positive for several…
We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot…
We consider embeddings of 3-regular graphs into 3-dimensional Cartesian coordinates, in such a way that two vertices are adjacent if and only if two of their three coordinates are equal (that is, if they lie on an axis-parallel line) and…
We study graph classes modeled by families of non-crossing (NC) connected sets. Two classic graph classes in this context are disk graphs and proper interval graphs. We focus on the cases when the sets are paths and the host is a tree…