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We study the problem of counting $k$-hypergraphlets, an interesting but surprisingly ignored primitive, with the aim of understanding whether efficient algorithms exist. To this end, we consider color coding, a well-known technique for…
This paper introduces an efficient quantum computing method for reducing special graphs in the context of the graph coloring problem. The special graphs considered include both symmetric and non-symmetric graphs where the axis passes…
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.…
We study quantum analogs of graph colorings and chromatic number. Initially defined via an interactive protocol, quantum colorings can also be viewed as a natural operator relaxation of graph coloring. Since there is no known algorithm for…
In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…
The applications of graph coloring are diverse and many so lots of new types of coloring are being proposed and explored. Here we define a safe k-coloring, motivated by the application of coloring to secret sharing. Secret sharing is a way…
The graph coloring problem (GCP) is one of the most studied NP-HARD problems in computer science. Given a graph , the task is to assign a color to all vertices such that no vertices sharing an edge receive the same color and that the number…
Given a large social or information network, how can we partition the vertices into sets (i.e., colors) such that no two vertices linked by an edge are in the same set while minimizing the number of sets used. Despite the obvious practical…
In graph coloring problems, the goal is to assign a positive integer color to each vertex of an input graph such that adjacent vertices do not receive the same color assignment. For classic graph coloring, the goal is to minimize the…
Bounded expansion and nowhere-dense classes of graphs capture the theoretical tractability for several important algorithmic problems. These classes of graphs can be characterized by the so-called weak coloring numbers of graphs, which…
Several authors modelled networks ad hoc by oriented or disoriented graphs, whereby the problem of allowance (allocation) of the frequencies at the level of the network was transformed into coloring problem of nodes in the graph. Graph…
In this paper we consider coloring problems on graphs and other combinatorial structures on standard Borel spaces. Our goal is to obtain sufficient conditions under which such colorings can be made well-behaved in the sense of topology or…
A graph is k-total colourable if there is an assignment of k different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour. The total chromatic number of some direct product…
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…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction…
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…
Differential Privacy is the gold standard in privacy-preserving data analysis. This paper addresses the challenge of producing a differentially edge-private vertex coloring. In this paper, we present two novel algorithms to approach this…
Graph colouring is a fundamental problem for networks, serving as a tool for avoiding conflicts via symmetry breaking, for example, avoiding multiple computer processes simultaneously updating the same resource. This paper considers a…
The state-of-the-art coding schemes for topological interference management (TIM) problems are usually handcrafted for specific families of network topologies, relying critically on experts' domain knowledge. This inevitably restricts the…