Related papers: Probabilistic Zero Forcing with Vertex Reversion
Vertex-Reinforced Random Walk (VRRW), defined by Pemantle (1988a), is a random process in a continuously changing environment which is more likely to visit states it has visited before. We consider VRRW on arbitrary graphs and show that on…
Graph coloring is a fundamental problem in combinatorics with many applications in practice. In this problem, the vertices in a given graph must be colored by using the least number of colors in such a way that a vertex has a different…
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…
Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…
Phase retrieval(PR) problem is a kind of ill-condition inverse problem which is arising in various of applications. Based on the Wirtinger flow(WF) method, a reweighted Wirtinger flow(RWF) method is proposed to deal with PR problem. RWF…
One method to obtain a proper vertex coloring of graphs using a reasonable number of colors is to start from any arbitrary proper coloring and then repeat some local re-coloring techniques to reduce the number of color classes. The Grundy…
We devise a new formulation for the vertex coloring problem. Different from other formulations, decision variables are associated with the pairs of vertices. Consequently, colors will be distinguishable. Although the objective function is…
We deal with a random graph model where at each step, a vertex is chosen uniformly at random, and it is either duplicated or its edges are deleted. Duplication has a given probability. We analyse the limit distribution of the degree of a…
We solve, in a fully decentralised way (\ie with no message passing), the classic problem of colouring a graph. We propose a novel algorithm that is automatically responsive to topology changes, and we prove that it converges quickly to a…
Each vertex of the infinite $2$-dimensional square lattice graph is assigned, independently, a label that reads trap with probability $p$, target with probability $q$, and open with probability $(1-p-q)$, and each edge is assigned,…
For an $n$-vertex graph $G$, let $z(G;k)$ denote the number of zero forcing sets of size $k$. A conjecture of Boyer et al. asserts that the path $P_n$ maximizes these numbers coefficientwise among all $n$-vertex graphs; equivalently, the…
There are a number of well-known problems and conjectures about partitioning graphs to satisfy local constraints. For example, the majority colouring conjecture of Kreutzer, Oum, Seymour, van der Zypen and Wood states that every directed…
We show a method how to convert any graph into the binary number and vice versa. We derive upper bound for maximum number of graphs, that, have fixed number of vertices and can be colored with n colors (n is any given number). Proof for the…
A k-edge-weighting of a graph G is a function w: E(G)->{1,2,...,k}. An edge-weighting naturally induces a vertex coloring c, where for every vertex v in V(G), c(v) is sum of weights of the edges that are adjacent to vertex v. If the induced…
In this paper, we initiate the study of the vertex coloring problem of a graph in the semi streaming model. In this model, the input graph is defined by a stream of edges, arriving in adversarial order and any algorithm must process the…
Circular coloring is a constraints satisfaction problem where colors are assigned to nodes in a graph in such a way that every pair of connected nodes has two consecutive colors (the first color being consecutive to the last). We study…
Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a…
The Glauber dynamics on the colourings of a graph is a random process which consists in recolouring at each step a random vertex of a graph with a new colour chosen uniformly at random among the colours not already present in its…
Let $S$ be a set of vertices of a graph $G$. Let $cl(S)$ be the set of vertices built from $S$, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in $cl(S)$, then the remaining…
While a number of bounds are known on the zero forcing number $Z(G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number…