Related papers: Neutrality in the Graph Coloring Problem
Graph Coloring is probably one of the most studied and famous problem in graph algorithms. Exact methods fail to solve instances with more than few hundred vertices, therefore, a large number of heuristics have been proposed. Nested Monte…
This paper presents a new methodology that exploits specific characteristics from the fitness landscape. In particular, we are interested in the property of neutrality, that deals with the fact that the same fitness value is assigned to…
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…
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal…
We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that…
Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…
A $k$-coloring of a graph is an assignment of integers between $1$ and $k$ to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further…
The interference imposes a significant negative impact on the performance of wireless networks. With the continuous deployment of larger and more sophisticated wireless networks, reducing interference in such networks is quickly being…
Motivated by understanding non-strict and strict pure strategy equilibria in network anti-coordination games, we define notions of stable and, respectively, strictly stable colorings in graphs. We characterize the cases when such colorings…
A \textit{locally identifying coloring} ($lid$-coloring) of a graph is a proper coloring such that the sets of colors appearing in the closed neighborhoods of any pair of adjacent vertices having distinct neighborhoods are distinct. Our…
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…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
In recent years, there has been a significant amount of research focused on expanding the expressivity of Graph Neural Networks (GNNs) beyond the Weisfeiler-Lehman (1-WL) framework. While many of these studies have yielded advancements in…
The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…
NP-complete problems should be hard on some instances but those may be extremely rare. On generic instances many such problems, especially related to random graphs, have been proven easy. We show the intractability of random instances of a…
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.…
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…
We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…
A proper vertex-colouring of a graph G is said to be locally identifying if for any pair u,v of adjacent vertices with distinct closed neighbourhoods, the sets of colours in the closed neighbourhoods of u and v are different. We show that…