Related papers: Online Multi-Coloring with Advice
A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding…
For a connected graph, we define the proper-walk connection number as the minimum number of colors needed to color the edges of a graph so that there is a walk between every pair of vertices without two consecutive edges having the same…
Inspired by the fact that spreading and collecting information through the Internet becomes the norm, more and more people choose to post for-profit contents (images and texts) in social networks. Due to the difficulty of network censors,…
State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.
In this paper, we present multi-threaded algorithms for graph coloring suitable to the shared memory programming model. We modify an existing algorithm widely used in the literature and prove the correctness of the modified algorithm. We…
We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kier- stead's algorithm for graphs that contain neither a C3 or C5 as an induced subgraph.
A locally irregular multigraph is a multigraph whose adjacent vertices have distinct degrees. The locally irregular edge coloring is an edge coloring of a multigraph $G$ such that every color induces a locally irregular submultigraph of…
Graph colorings are becoming an increasingly useful family of mathematical models for a broad range of applications, such as time tabling and scheduling, frequency assignment, register allocation, computer security and so on. Graph proper…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to…
Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if…
This paper considers the problem of network coding for multiple unicast connections in networks represented by directed acyclic graphs. The concept of interference alignment, traditionally used in interference networks, is extended to…
A rainbow colouring of a connected graph is a colouring of the edges of the graph, such that every pair of vertices is connected by at least one path in which no two edges are coloured the same. Such a colouring using minimum possible…
In this paper, we consider the problem of a star coloring. In general case the problems in NP-complete. We establish the star chromatic number for splitting graph of complete and complete bipartite graphs, as well of paths and cycles. Our…
The present work deals with the problem of efficiently assigning Wi-Fi channels in a real-world scenario, the Polytechnic School of the University of Alcal\'a. We first use proximity graphs to model the whole problem as an instance of…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
Many real world networks have groups of similar nodes which are vulnerable to the same failure or adversary. Nodes can be colored in such a way that colors encode the shared vulnerabilities. Using multiple paths to avoid these…
Graph Coloring consists in assigning colors to vertices ensuring that two adjacent vertices do not have the same color. In dynamic graphs, this notion is not well defined, as we need to decide if different colors for adjacent vertices must…
Graph workloads pose a particularly challenging problem for query optimizers. They typically feature large queries made up of entirely many-to-many joins with complex correlations. This puts significant stress on traditional cardinality…
This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph…