Related papers: On Colorful Vertex and Edge Cover Problems
The widely studied edge modification problems ask how to minimally alter a graph to satisfy certain structural properties. In this paper, we introduce and study a new edge modification problem centered around transforming a given graph into…
This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…
In an edge-colored graph, a traversal cost occurs at a vertex along a path when consecutive edges with different colors are traversed. The value of the traversal cost depends only on the colors of the traversed edges. This concept leads to…
We consider the single-conflict coloring problem, a graph coloring problem in which each edge of a graph receives a forbidden ordered color pair. The task is to find a vertex coloring such that no two adjacent vertices receive a pair of…
This paper continues the study of a new variant of graph coloring with a connectivity constraint recently introduced by Hsieh et al. [COCOON 2024]. A path in a vertex-colored graph is called conflict-free if there is a color that appears…
Given an ordering of the vertices of a graph, the cost of covering an edge is the smaller number of its two ends. The minimum sum vertex cover problem asks for an ordering that minimizes the total cost of covering all edges. We consider…
Minimum sum vertex cover of an $n$-vertex graph $G$ is a bijection $\phi : V(G) \to [n]$ that minimizes the cost $\sum_{\{u,v\} \in E(G)} \min \{\phi(u), \phi(v) \}$. Finding a minimum sum vertex cover of a graph (the MSVC problem) is…
Given a graph $G=(V,E)$ and a positive integer $t\geq2$, the task in the vertex cover $P_t$ ($VCP_t$) problem is to find a minimum subset of vertices $F\subseteq V$ such that every path of order $t$ in $G$ contains at least one vertex from…
We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…
The quest for colorful components (connected components where each color is associated with at most one vertex) inside a vertex-colored graph has been widely considered in the last ten years. Here we consider two variants, Minimum Colorful…
The input of the Maximum Colored Cut problem consists of a graph $G=(V,E)$ with an edge-coloring $c:E\to \{1,2,3,\ldots , p\}$ and a positive integer $k$, and the question is whether $G$ has a nontrivial edge cut using at least $k$ colors.…
In this paper, we propose a new family of graphs, matrix graphs, whose vertex set $\mathbb{F}^{N\times n}_q$ is the set of all $N\times n$ matrices over a finite field $\mathbb{F}_q$ for any positive integers $N$ and $n$. And any two…
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…
We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via…
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…
The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most $k$ that induces a connected subgraph of $G$. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in…
The Minimum Coloring Cut Problem is defined as follows: given a connected graph G with colored edges, find an edge cut E' of G (a minimal set of edges whose removal renders the graph disconnected) such that the number of colors used by the…
Given an $r$-edge-coloured complete graph $K_n$, how many monochromatic connected components does one need in order to cover its vertex set? This natural question is a well-known essentially equivalent formulation of the classical Ryser's…
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…
Generally, a graph G, an independent set is a subset S of vertices in G such that no two vertices in S are adjacent (connected by an edge) and a vertex cover is a subset S of vertices such that each edge of G has at least one of its…