Related papers: Graph Coloring via Quantum Optimization on a Rydbe…
In vertex recoloring, we are given $n$ vertices with their initial coloring, and edges arrive in an online fashion. The algorithm must maintain a valid coloring by recoloring vertices, at a cost. The problem abstracts a scenario of job…
In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…
We introduce a qubit- and gate-efficient higher-order unconstrained binary optimization (HUBO) encoding for graph partitioning problems requiring label-count minimization. This widely applicable class of problems includes minimum graph…
This paper explores the application of a new algebraic method of color exchanges to the edge coloring of simple graphs. Vizing's theorem states that the edge coloring of a simple graph $G$ requires either $\Delta$ or $\Delta+1$ colors,…
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…
Independently posed by Behzad and Vizing, the Total Coloring Conjecture asserts that the total chromatic number of a simple connected graph $G$ is either $\Delta(G)+1$ or $\Delta(G)+2$, where $\Delta(G)$ is the largest degree of any vertex…
Transformers are increasingly employed for graph data, demonstrating competitive performance in diverse tasks. To incorporate graph information into these models, it is essential to enhance node and edge features with positional encodings.…
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the…
In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color…
We study the maximization version of the fundamental graph coloring problem. Here the goal is to color the vertices of a k-colorable graph with k colors so that a maximum fraction of edges are properly colored (i.e. their endpoints receive…
In this paper, we present multi-threaded algorithms for graph coloring suitable to the shared memory programming model. We modify an existing algorithm widely used in the literature and prove the correctness of the modified algorithm. We…
List colouring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening of this problem, where instead of one list-colouring, we seek many in parallel. Our explorations have uncovered a…
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter…
In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve…
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…
We present a blueprint for building a fault-tolerant universal quantum computer with Rydberg atoms. Our scheme, which is based on the surface code, uses individually-addressable optically-trapped atoms as qubits and exploits…
The rapid development of neutral atom quantum hardware provides a unique opportunity to design hardware-centered algorithms for solving real-world problems aimed at establishing quantum utility. In this work, we study the performance of two…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
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…