Related papers: Complexity of Modification Problems for Reciprocal…
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…
Recent investigations in computational biology focus on a family of 2-colored digraphs, called 2-colored best match graphs, which naturally arise from rooted phylogenetic trees. Actually the defining properties of such graphs are…
Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation…
The anti-Ramsey number, $ar(G, H)$ is the minimum integer $k$ such that in any edge colouring of $G$ with $k$ colours there is a rainbow subgraph isomorphic to $H$, i.e., a copy of $H$ with each of its edges assigned a different colour. The…
We study the rainbow matching (RM) problem: given an edge-colored graph, find a maximum matching with at most one edge of each color. Rainbow matchings correspond to stable sets in the \emph{augmented} graph $H$ obtained from the line graph…
Cographs are graphs in which no four vertices induce a simple connected path $P_4$. Cograph editing is to find for a given graph $G = (V,E)$ a set of at most $k$ edge additions and deletions that transform $G$ into a cograph. This…
Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to…
In this paper, we study orthogonal colourings of random geometric graphs. Two colourings of a graph are orthogonal if they have the property that when two vertices receive the same colour in one colouring, then those vertices receive…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
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,…
We study the problem of determining whether a given graph~$G=(V,E)$ admits a matching~$M$ whose removal destroys all odd cycles of~$G$ (or equivalently whether~$G-M$ is bipartite). This problem is equivalent to determine whether~$G$ admits…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A homomorphism from edge-coloured graph $G$ to edge-coloured graph $H$ is a vertex-mapping from $G$ to…
Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…
In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…