相关论文: Motions on n-Simplex Graphs with m-value memory
Identifying the sets of operations that can be executed simultaneously is an important problem appearing in many parallel applications. By modeling the operations and their interactions as a graph, one can identify the independent…
In chomp on graphs, two players alternatingly pick an edge or a vertex from a graph. The player that cannot move any more loses. The questions one wants to answer for a given graph are: Which player has a winning strategy? Can a explicit…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
For any fixed surface Sigma of genus g, we give an algorithm to decide whether a graph G of girth at least five embedded in Sigma is colorable from an assignment of lists of size three in time O(|V(G)|). Furthermore, we can allow a subgraph…
A proper vertex colouring of a graph is \emph{nested} if the vertices of each of its colour classes can be ordered by inclusion of their open neighbourhoods. Through a relation to partially ordered sets, we show that the nested chromatic…
Graph Coloring consists in assigning colors to vertices ensuring that two adjacent vertices do not have the same color. In dynamic graphs, this notion is not well defined, as we need to decide if different colors for adjacent vertices must…
Which graphs, in the class of all graphs with given numbers n and m of edges and vertices respectively, minimizes or maximizes the value of some graph parameter? In this paper we develop a technique which provides answers for several…
Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
We introduce two novel evolutionary formulations of the problem of coloring the nodes of a graph. The first formulation is based on the relationship that exists between a graph's chromatic number and its acyclic orientations. It views such…
The Colouring problem is that of deciding, given a graph $G$ and an integer $k$, whether $G$ admits a (proper) $k$-colouring. For all graphs $H$ up to five vertices, we classify the computational complexity of Colouring for…
We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the…
We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…
A graph $G$ is called uniquely k-list colorable (U$k$LC) if there exists a list of colors on its vertices, say $L=\lbrace S_v \mid v \in V(G) \rbrace $, each of size $k$, such that there is a unique proper list coloring of $G$ from this…
We say that a graph is $k$-mixing if it is possible to transform any $k$-coloring into any other via a sequence of single vertex recolorings keeping a proper coloring all along. Cereceda, van den Heuvel and Johnson proved that deciding if a…
We investigate three formalisms to specify graph languages, i.e. sets of graphs, based on type graphs. First, we are interested in (pure) type graphs, where the corresponding language consists of all graphs that can be mapped…
3-list colouring is an NP-complete decision problem. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list colouring on permutation graphs.
We introduce the notion of a move graph, that is, a directed graph whose vertex set is a $\mathbb Z$-module $\mathbb Z_n^m$, and whose arc set is uniquely determined by the action $M\!:\!\mathbb Z_n^m\to \mathbb Z_n^m$ where $M$ is an…
Edge lengths of a graph are called flexible if there exist infinitely many non-congruent realizations of the graph in the plane satisfying these edge lengths. It has been shown recently that a graph has flexible edge lengths if and only if…
Graph Coloring is probably one of the most studied and famous problem in graph algorithms. Exact methods fail to solve instances with more than few hundred vertices, therefore, a large number of heuristics have been proposed. Nested Monte…