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One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
Research on graph representation learning has received a lot of attention in recent years since many data in real-world applications come in form of graphs. High-dimensional graph data are often in irregular form, which makes them more…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
Learning faithful graph representations as sets of vertex embeddings has become a fundamental intermediary step in a wide range of machine learning applications. The quality of the embeddings is usually determined by how well the geometry…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…
Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluation of scatterplots such as scagnostics have been presented and applied to…
Graph embedding aims at learning a vector-based representation of vertices that incorporates the structure of the graph. This representation then enables inference of graph properties. Existing graph embedding techniques, however, do not…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Graph coloring involves assigning colors to the vertices of a graph such that two vertices linked by an edge receive different colors. Graph coloring problems are general models that are very useful to formulate many relevant applications…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Graph embeddings, wherein the nodes of the graph are represented by points in a continuous space, are used in a broad range of Graph ML applications. The quality of such embeddings crucially depends on whether the geometry of the space…