Related papers: Finding Colorful Paths in Temporal Graphs
Graph colouring is a fundamental problem for networks, serving as a tool for avoiding conflicts via symmetry breaking, for example, avoiding multiple computer processes simultaneously updating the same resource. This paper considers a…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Temporal graphs are graphs whose topology is subject to discrete changes over time. Given a static underlying graph $G$, a temporal graph is represented by assigning a set of integer time-labels to every edge $e$ of $G$, indicating the…
Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…
A classic graph coloring problem is to assign colors to vertices of any graph so that distinct colors are assigned to adjacent vertices. Optimal graph coloring colors a graph with a minimum number of colors, which is its chromatic number.…
We investigate the relationship between two kinds of vertex colorings of graphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color…
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…
We consider the maximum chromatic number of hypergraphs consisting of cliques that have pairwise small intersections. Designs of the appropriate parameters produce optimal constructions, but these are known to exist only when the number 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…
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the…
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph.…
A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs…
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P…
Colouring sparse graphs under various restrictions is a theoretical problem of significant practical relevance. Here we consider the problem of maximizing the number of different colours available at the nodes and their neighbourhoods,…
A well-studied coloring problem is to assign colors to the edges of a graph $G$ so that, for every pair of vertices, all edges of at least one shortest path between them receive different colors. The minimum number of colors necessary in…
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…
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do…
We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…
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…