相关论文: A matheuristic approach for the $b$-coloring probl…

A b-coloring of a graph $G$ is a coloring of its vertices such that every color class contains a vertex that has neighbors in all other classes. The b-chromatic number of $G$ is the largest integer $k$ such that $G$ has a b-coloring with…

In an undirected graph, a proper (k,i)-coloring is an assignment of a set of k colors to each vertex such that any two adjacent vertices have at most i common colors. The (k,i)-coloring problem is to compute the minimum number of colors…

Let $G = (V,E)$ be a finite simple graph. Recall that a proper coloring of $G$ is a mapping $\varphi: V\to\{1,\ldots,k\}$ such that every color class induces an independent set. Such a $\varphi$ is called a semi-matching coloring if the…

A dominating set D in a graph G is a subset of its vertices such that every vertex of the graph which does not belong to set D is adjacent to at least one vertex from set D. A set of vertices of graph G is a global dominating set if it is a…

This paper investigates an extremely classic NP-complete problem: How to determine if a graph G, where each vertex has a degree of at most 4, can be 3-colorable(The research in this paper focuses on graphs G that satisfy the condition where…

Let $G$ be a graph and $t$ a nonnegative integer. Suppose $f$ is a mapping from the vertex set of $G$ to $\{1,2,\dots, k\}$. If, for any vertex $u$ of $G$, the number of neighbors $v$ of $u$ with $f(v)=f(u)$ is less than or equal to $t$,…

Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics and can be approximated with the help of similarity measures between gene sequences, albeit not without errors. The corresponding…

Graph burning is a process of information spreading through the network by an agent in discrete steps. The problem is to find an optimal sequence of nodes which have to be given information so that the network is covered in least number of…

Combinatorial optimization problems near algorithmic phase transitions represent a fundamental challenge for both classical algorithms and machine learning approaches. Among them, graph coloring stands as a prototypical constraint…

The problems studied in this paper originate from Graph Motif, a problem introduced in 2006 in the context of biological networks. Informally speaking, it consists in deciding if a multiset of colors occurs in a connected subgraph of a…

In this paper we consider a variation of a recoloring problem, called the Color-Fixing. Let us have some non-proper $r$-coloring $\varphi$ of a graph $G$. We investigate the problem of finding a proper $r$-coloring of $G$, which is "the…

The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have…

We investigate the List $H$-Coloring problem, the generalization of graph coloring that asks whether an input graph $G$ admits a homomorphism to the undirected graph $H$ (possibly with loops), such that each vertex $v \in V(G)$ is mapped to…

The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…

The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for…

In the Selective Coloring problem, we are given an integer $k$, a graph $G$, and a partition of $V(G)$ into $p$ parts, and the goal is to decide whether or not we can pick exactly one vertex of each part and obtain a $k$-colorable induced…

In this paper we consider colorings of oriented graphs, i.e. digraphs without cycles of length 2. Given some oriented graph $G=(V,E)$, an oriented $r$-coloring for $G$ is a partition of the vertex set $V$ into $r$ independent sets, such…

Let $G(V,E)$ be a $k$-uniform hypergraph. A hyperedge $e \in E$ is said to be properly $(r,p)$ colored by an $r$-coloring of vertices in $V$ if $e$ contains vertices of at least $p$ distinct colors in the $r$-coloring. An $r$-coloring of…

The Graph Motif problem was introduced in 2006 in the context of biological networks. It consists of deciding whether or not a multiset of colors occurs in a connected subgraph of a vertex-colored graph. Graph Motif has been mostly analyzed…

A b-coloring of a graph is a proper coloring such that each color class has at least one vertex which is adjacent to each other color class. The b-spectrum of $G$ is the set $S_{b}(G)$ of integers $k$ such that $G$ has a b-coloring with $k$…