Related papers: Color: A Framework for Applying Graph Coloring to …
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…
In the $\ell$-Coloring Problem, we are given a graph on $n$ nodes, and tasked with determining if its vertices can be properly colored using $\ell$ colors. In this paper we study below-guarantee graph coloring, which tests whether an…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Colour refinement is a basic algorithmic routine for graph isomorphism testing, appearing as a subroutine in almost all practical isomorphism solvers. It partitions the vertices of a graph into "colour classes" in such a way that all…
Color Refinement, also known as Naive Vertex Classification, is a classical method to distinguish graphs by iteratively computing a coloring of their vertices. While it is mainly used as an imperfect way to test for isomorphism, the…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
Graph coloring has been broadly used to discover concurrency in parallel computing. To speedup graph coloring for large-scale datasets, parallel algorithms have been proposed to leverage modern GPUs. Existing GPU implementations either have…
E-graphs are a prominent data structure that has been increasing in popularity in recent years due to their expanding range of applications in various formal reasoning tasks. Often, they are used for equality saturation, a process of…
In the context of the chromatic-number problem, a critical graph is an instance where the deletion of any element would decrease the graph's chromatic number. Such instances have shown to be interesting objects of study for deepen the…
Conformal prediction provides rigorous, distribution-free uncertainty guarantees, but often yields prohibitively large prediction sets in structured domains such as routing, planning, or sequential recommendation. We introduce "graph-based…
One of the fundamental and most-studied algorithmic problems in distributed computing on networks is graph coloring, both in bounded-degree and in general graphs. Recently, the study of this problem has been extended in two directions.…
In this paper we study threshold coloring of graphs, where the vertex colors represented by integers are used to describe any spanning subgraph of the given graph as follows. Pairs of vertices with near colors imply the edge between them is…
In this work we focus on the problem of colorization for image compression. Since color information occupies a large proportion of the total storage size of an image, a method that can predict accurate color from its grayscale version can…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Modern deep models have massive parameter sizes, leading to high inference-time memory usage that limits practical deployment. Parameter sharing, a form of structured compression, effectively reduces redundancy, but existing approaches…
We introduce learning augmented algorithms to the online graph coloring problem. Although the simple greedy algorithm FirstFit is known to perform poorly in the worst case, we are able to establish a relationship between the structure of…
We consider the subgraph isomorphism problem where, given two graphs G (source graph) and F (pattern graph), one is to decide whether there is a (not necessarily induced) subgraph of G isomorphic to F. While many practical heuristic…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Given an undirected graph $G=(V,E)$ with a set of vertices $V$ and a set of edges $E$, a graph coloring problem involves finding a partition of the vertices into different independent sets. In this paper we present a new framework that…
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…