Related papers: Color Refinement for Relational Structures
Image colorization, the task of adding colors to grayscale images, has been the focus of significant research efforts in computer vision in recent years for its various application areas such as color restoration and automatic animation…
The graph coloring problem (GCP) is a classic combinatorial optimization problem that aims to find the minimum number of colors assigned to vertices of a graph such that no two adjacent vertices receive the same color. GCP has been…
The paper considers the NP-hard graph vertex coloring problem, which differs from traditional problems in which it is required to color vertices with a given (or minimal) number of colors so that adjacent vertices have different colors. In…
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…
A $k$-coloring of a graph $G$ is a partition of the set of vertices of $G$ into $k$ independent sets, which are called colors. A $k$-coloring is neighbor-locating if any two vertices belonging to the same color can be distinguished from…
A distinguishing coloring of a graph is a vertex coloring such that only the identity automorphism of the graph preserves the coloring. A 2-distinguishable graph is a graph which can be distinguished using 2 colors. The cost $\rho(G)$ of a…
An $n$-vertex graph is equitably $k$-colorable if there is a proper coloring of its vertices such that each color is used either $\left\lfloor n/k \right\rfloor$ or $\left\lceil n/k \right\rceil$ times. While classic Vertex Coloring is…
An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a…
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…
A vertex-colored graph is {\it rainbow vertex-connected} if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\it rainbow vertex-connection} of a…
We study how the complexity of the graph colouring problems star colouring and restricted star colouring vary with the maximum degree of the graph. Restricted star colouring (in short, rs colouring) is a variant of star colouring. For $k\in…
Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known…
Network alignment, or the task of finding meaningful node correspondences between nodes in different graphs, is an important graph mining task with many scientific and industrial applications. An important principle for network alignment is…
Advanced graph neural networks have shown great potentials in graph classification tasks recently. Different from node classification where node embeddings aggregated from local neighbors can be directly used to learn node labels, graph…
Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For $\alpha \leq 1$ and $k \in \mathbb{Z}^+$, we say that a graph $G=(V,E)$ is…
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…
Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in…
Graph Neural Networks (GNNs) are widely adopted in Web-related applications, serving as a core technique for learning from graph-structured data, such as text-attributed graphs. Yet in real-world scenarios, such graphs exhibit deficiencies…
In graph self-supervised learning, masked autoencoders (MAE) and contrastive learning (CL) are two prominent paradigms. MAE focuses on reconstructing masked elements, while CL maximizes similarity between augmented graph views. Recent…