Related papers: Choosing Colors for Geometric Graphs via Color Spa…
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The…
Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
Subgraph matching is vital in knowledge graph (KG) question answering, molecule design, scene graph, code and circuit search, etc. Neural methods have shown promising results for subgraph matching. Our study of recent systems suggests…
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
We study a weighted-set graph coloring problem in which one assigns $q$ colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting $w$ that either disfavors or favors a given subset of $s$…
We investigate an algebraic problem related to the determination of the fundamental group of a class of spaces of configurations on surfaces. The configuration spaces are spaces of points grouped into colors. Whether two points are allowed…
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 colorings is a fundamental topic in graph theory that require an assignment of labels (or colors) to vertices or edges subject to various constraints. We focus on the harmonious coloring of a graph, which is a proper vertex coloring…
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…
Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the…
Drawing principles, or aesthetics, are important in graph drawing. They are used as criteria for algorithm design and for quality evaluation. Current aesthetics are described as visual properties that a drawing is required to have to be…
We examine maximum vertex coloring of random geometric graphs, in an arbitrary but fixed dimension, with a constant number of colors. Since this problem is neither scale-invariant nor smooth, the usual methodology to obtain limit laws…
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…
The \emph{Square Colouring} of a graph $G$ refers to colouring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colours. In this paper, we initiate the study of a related…
Set-coloring a graph means giving each vertex a subset of a fixed color set so that no two adjacent subsets have the same cardinality. When the graph is complete one gets a new distribution problem with an interesting generating function.…
In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…
In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
A set of colored graphs are compatible, if for every color $i$, the number of vertices of color $i$ is the same in every graph. A simultaneous embedding of $k$ compatibly colored graphs, each with $n$ vertices, consists of $k$ planar…