Related papers: Recognizing embedded caterpillars with weak unit d…
We prove that determining the weak saturation number of a host graph $F$ with respect to a pattern graph $H$ is already a computationally hard problem when $H$ is the triangle. As our main tool we establish a connection between weak…
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…
There is a recent interest in neural network (NN)-based communication algorithms which have shown to achieve (beyond) state-of-the-art performance for a variety of problems or lead to reduced implementation complexity. However, most work on…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
A graph $G$ is a $B_0$-VPG graph if one can associate a path on a rectangular grid with each vertex such that two vertices are adjacent if and only if the corresponding paths intersect at at least one grid-point. A graph $G$ is a contact…
For a fixed property (graph class) ${\Pi}$, given a graph G and an integer k, the ${\Pi}$-deletion problem consists in deciding if we can turn $G$ into a graph with the property ${\Pi}$ by deleting at most $k$ edges. The ${\Pi}$-deletion…
Assume that a graph $G$ models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a…
Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Patch-level image representation is very important for object classification and detection, since it is robust to spatial transformation, scale variation, and cluttered background. Many existing methods usually require fine-grained…
In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are…
We improve the best known upper bound on the number of edges in a unit-distance graph on $n$ vertices for each $n\in\{16,\ldots,30\}$. When $n\leq 21$, our bounds match the best known lower bounds, and we fully enumerate the densest…
Let $\beta>0$. Motivated by jumbled graphs defined by Thomason, the celebrated expander mixing lemma and Haemers's vertex separation inequality, we define that a graph $G$ with $n$ vertices is a weakly $(n,\beta)$-graph if $\frac{|X|…
The Joint Crossing Number problem asks for a simultaneous embedding of two disjoint graphs into one surface such that the number of edge crossings (between the two graphs) is minimized. It was introduced by Negami in 2001 in connection with…
Contraction of an edge merges its end points into a new vertex which is adjacent to each neighbor of the end points of the edge. An edge in a $k$-connected graph is {\em contractible} if its contraction does not result in a graph of lower…
A graph is called (generically) rigid in R^d if, for any choice of sufficiently generic edge lengths, it can be embedded in R^d in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining…
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called $B_0$-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time…
Network embedding is a highly effective method to learn low-dimensional node vector representations with original network structures being well preserved. However, existing network embedding algorithms are mostly developed for a single…
Photonic integration of thick holograms in waveguiding structures could be considered the chimera of photonics; multi-faceted and hard to tame. It is the fundamental, and hence indispensable, concept behind compact and monolithically…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once-punctured polygons which, in turn, contain all possible geometric flip-graphs of…