Related papers: Intensive use of computing resources for dominatio…
In this paper, we investigate the \textsc{Grundy Coloring} problem for graphs with a cluster modulator, a structure commonly found in dense graphs. The Grundy chromatic number, representing the maximum number of colors needed for the…
This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…
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…
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…
We study the dominating set problem in an online setting. An algorithm is required to guarantee competitiveness against an adversary that reveals the input graph one node at a time. When a node is revealed, the algorithm learns about the…
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…
A $k$-coloring of a tournament is a partition of its vertices into $k$ acyclic sets. Deciding if a tournament is 2-colorable is NP-hard. A natural problem, akin to that of coloring a 3-colorable graph with few colors, is to color a…
The domination problem and its variants represent a classical domain within algorithmic graph theory. Among these variants, the paired-domination problem holds particular prominence due to its real-world implications in security and…
We consider vertex colorings of graphs in which adjacent vertices have distinct colors. A graph is $s$-chromatic if it is colorable in $s$ colors and any coloring of it uses at least $s$ colors. The forcing chromatic number $F(G)$ of an…
In this paper, we investigate the impact of the broadcast effect arising in filterless optical networks on the computational complexity of the wavelength assignment problem. We model conflicts using an appropriate interference digraph,…
Vizing's theorem states that every graph $G$ of maximum degree $\Delta$ can be properly edge-colored using $\Delta + 1$ colors. The fastest currently known $(\Delta+1)$-edge-coloring algorithm for general graphs is due to Sinnamon and runs…
We introduce a new topological encoding of executions of round-based, full-information distributed protocols via spectral spaces. Such protocols constitute a model of distributed computations which are functorially presented and englobe…
We survey recent (and not so recent) results concerning arrangements of lines, points and other geometric objects and the applications these results have in theoretical computer science and combinatorics. The three main types of problems we…
The graph coloring problem asks for an assignment of the minimum number of distinct colors to vertices in an undirected graph with the constraint that no pair of adjacent vertices share the same color. The problem is a thoroughly studied…
The \emph{Square Colouring} of a graph $G$ refers to colouring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colours. In this paper, we initiate the study of a related…
We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
We present the Douglas-Rachford algorithm as a successful heuristic for solving graph coloring problems. Given a set of colors, these type of problems consist in assigning a color to each node of a graph, in such a way that every pair of…
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…
The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…