Related papers: Color Refinement for Relational Structures

Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure.…

In order to make more complex number-based strings from topological coding for defending against the intelligent attacks equipped with quantum computing and providing effective protection technology for the age of quantum computing, we will…

Unsupervised cell type identification is crucial for uncovering and characterizing heterogeneous populations in single cell omics studies. Although a range of clustering methods have been developed, most focus exclusively on intrinsic…

Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…

Texture classification became one of the problems which has been paid much attention on by image processing scientists since late 80s. Consequently, since now many different methods have been proposed to solve this problem. In most of these…

Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to…

A colored graph is a directed graph in which nodes or edges have been assigned colors that are not necessarily unique. Observability problems in such graphs consider whether an agent observing the colors of edges or nodes traversed on a…

Color and structure are the two pillars that combine to give an image its meaning. Interested in critical structures for neural network recognition, we isolate the influence of colors by limiting the color space to just a few bits, and find…

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 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…

Relation reasoning in knowledge graphs (KGs) aims at predicting missing relations in incomplete triples, whereas the dominant paradigm is learning the embeddings of relations and entities, which is limited to a transductive setting and has…

Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…

Fix a graph $G$ in which every edge is colored in some of $k\ge 2$ colors. Two vertices $u$ and $v$ are CA-connected if $u$ and $v$ may be connected using any subset of $k - 1$ colors. CA-connectivity is an equivalence relation dividing the…

We propose Graph Consistency Regularization (GCR), a novel framework that injects relational graph structures, derived from model predictions, into the learning process to promote class-aware, semantically meaningful feature…

I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…

Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A…

A linear coloring of a graph is a proper coloring of the vertices of the graph so that each pair of color classes induce a union of disjoint paths. In this paper, we prove that for every connected graph with maximum degree at most three and…

The CFI-graphs, named after Cai, F\"urer, and Immerman, are central to the study of the graph isomorphism testing and of first-order logic with counting. They are colored graphs, and the coloring plays a role in many of their applications.…

Color and structure are the two pillars that construct an image. Usually, the structure is well expressed through a rich spectrum of colors, allowing objects in an image to be recognized by neural networks. However, under extreme…

Image forensics, aiming to ensure the authenticity of the image, has made great progress in dealing with common image manipulation such as copy-move, splicing, and inpainting in the past decades. However, only a few researchers pay…