Related papers: Cyclic Shift Problems on Graphs

We consider the selective graph coloring problem, which is a generalization of the classical graph coloring problem. Given a graph together with a partition of its vertex set into clusters, we want to choose exactly one vertex per cluster…

In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…

Vertex coloring and multicoloring of graphs are a well known subject in graph theory, as well as their applications. In vertex multicoloring, each vertex is assigned some subset of a given set of colors. Here we propose a new kind of vertex…

Here we introduce a new game on graphs, called cup stacking, following a line of what can be considered as $0$-, $1$-, or $2$-person games such as chip firing, percolation, graph burning, zero forcing, cops and robbers, graph pebbling, and…

Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…

In the Minimum Bisection problem, input is a graph $G$ and the goal is to partition the vertex set into two parts $A$ and $B$, such that $||A|-|B|| \le 1$ and the number $k$ of edges between $A$ and $B$ is minimized. This problem can be…

The Colored Points Traveling Salesman Problem (Colored Points TSP) is introduced in this work as a novel variation of the traditional Traveling Salesman Problem (TSP) in which the set of points is partitioned into multiple classes, each of…

We introduce a dynamic version of the NP-hard graph problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a…

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…

We study a variation of the graph colouring problem on random graphs of finite average connectivity. Given the number of colours, we aim to maximise the number of different colours at neighbouring vertices (i.e. one edge distance) of any…

We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in…

In the solution discovery variant of a vertex (edge) subset problem $\Pi$ on graphs, we are given an initial configuration of tokens on the vertices (edges) of an input graph $G$ together with a budget $b$. The question is whether we can…

We modify the Pearce-Kelly algorithm that maintains a topological ordering for a directed acyclic graph in order to allow cycles to be tolerated. Cycles make topological orderings moot, of course, however tolerating them is useful in…

In the List $k$-Coloring problem we are given a graph whose every vertex is equipped with a list, which is a subset of $\{1,\ldots,k\}$. We need to decide if $G$ admits a proper coloring, where every vertex receives a color from its list.…

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…

Graph coloring, also known as vertex coloring, considers the problem of assigning colors to the nodes of a graph such that adjacent nodes do not share the same color. The optimization version of the problem concerns the minimization of the…

The graph reconstruction conjecture asserts that every simple graph on at least three vertices is uniquely determined by its deck of vertex-deleted subgraphs. In this expository article we survey the conjecture and present an…

Facility location problems on graphs are ubiquitous in real world and hold significant importance, yet their resolution is often impeded by NP-hardness. Recently, machine learning methods have been proposed to tackle such classical…

Scheduling wireless links for simultaneous activation in such a way that all transmissions are successfully decoded at the receivers and moreover network capacity is maximized is a computationally hard problem. Usually it is tackled by…

In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…