Related papers: Online Multi-Coloring with Advice

Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…

A proper vertex colouring of a graph is \emph{nested} if the vertices of each of its colour classes can be ordered by inclusion of their open neighbourhoods. Through a relation to partially ordered sets, we show that the nested chromatic…

In this paper we present matrix game-theoretic models for joint routing, network coding, and scheduling problem. First routing and network coding are modeled by using a new approach based on compressed topology matrix that takes into…

Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is…

Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…

Bipartite networks serve as highly suitable models to represent systems involving interactions between two distinct types of entities, such as online dating platforms, job search services, or ecommerce websites. These models can be…

Graph neural networks have been widely used for learning representations of nodes for many downstream tasks on graph data. Existing models were designed for the nodes on a single graph, which would not be able to utilize information across…

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…

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a…

Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…

Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…

An edge-weighting of a graph is called vertex-coloring if the weighted degrees yield a proper vertex coloring of the graph. It is conjectured that for every graph without isolated edge, a vertex-coloring edge-weighting with the set {1,2,3}…

Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…

We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use $2\log_2 n - 10$ colors, where $n$ is the number of vertices in the…

This paper introduces a natural generalization of the classical edge coloring problem in graphs that provides a useful abstraction for two well-known problems in multicast switching. We show that the problem is NP-hard and evaluate the…

How to utilize deep learning methods for graph classification tasks has attracted considerable research attention in the past few years. Regarding graph classification tasks, the graphs to be classified may have various graph sizes (i.e.,…

The online list coloring is a widely studied topic in graph theory. A graph $G$ is 2-paintable if we always have a strategy to complete a coloring in an online list coloring of $G$ in which each vertex has a color list of size 2. In this…

An edge colouring of a multigraph can be thought of as a partition of the edges into matchings (a matching meets each vertex at most once). Analogously, an edge cover colouring is a partition of the edges into edge covers (an edge cover…

We extend the concept of graph isomorphisms to multilayer networks with any number of "aspects" (i.e., types of layering). In developing this generalization, we identify multiple types of isomorphisms. For example, in multilayer networks…

Graph neural networks (GNNs) have gained prominence in recommendation systems in recent years. By representing the user-item matrix as a bipartite and undirected graph, GNNs have demonstrated their potential to capture short- and…