Related papers: Fair Short Paths in Vertex-Colored Graphs
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the…
Given an edge-coloring of a graph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. We define the palette index of a graph as the minimum number of distinct palettes, taken over all…
The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that for all vertices v the color of v is different from the color of any of its neighbors. The problem is NP-hard.…
In the present paper, we study algorithmic questions for the arc-intersection graph of directed paths on a tree. Such graphs are known to be perfect (proved by Monma and Wei in 1986). We present faster algorithms than all previously known…
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…
Algorithmic fairness has aroused considerable interests in data mining and machine learning communities recently. So far the existing research has been mostly focusing on the development of quantitative metrics to measure algorithm…
An assignment of colours to the vertices of a graph is stable if any two vertices of the same colour have identically coloured neighbourhoods. The goal of colour refinement is to find a stable colouring that uses a minimum number of…
The classic greedy coloring (first-fit) algorithm considers the vertices of an input graph $G$ in a given order and assigns the first available color to each vertex $v$ in $G$. In the {\sc Grundy Coloring} problem, the task is to find an…
A simple but empirically efficient heuristic algorithm for the edge-coloring of graphs is presented. Its basic idea is the displacement of "conflicts" (repeated colors in the edges incident to a vertex) along paths of adjacent vertices…
Temporal graphs are graphs with time-stamped edges. We study the problem of finding a small vertex set (the separator) with respect to two designated terminal vertices such that the removal of the set eliminates all temporal paths…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
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…
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more…
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…
We introduce and explore a family of vertex-coloring problems which, surprisingly enough, have not been considered before despite stemming from the problem of Wi-Fi channel assignment. Given a spectrum of colors, endowed with a matrix of…
This paper studies the problem of proper-walk connection number: given an undirected connected graph, our aim is to colour its edges with as few colours as possible so that there exists a properly coloured walk between every pair of…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
We study a new variant of graph coloring by adding a connectivity constraint. A path in a vertex-colored graph is called conflict-free if there is a color that appears exactly once on its vertices. A connected graph $G$ is said to be…
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…