For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. W...
Chip-firing is a combinatorial game played on an undirected graph in which we place chips on vertices. We study chip-firing on an infinite binary tree in which we add a self-loop to the root to ensure each vertex has degree 3. A vertex can fire if th...
In this paper, we investigate the parking process on a uniform random rooted binary tree with $n$ vertices. Viewing each vertex as a single parking space, a random number of cars independently arrive at and attempt to park on each vertex one at a tim...
A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs when the nu...
The paper deals with a polling game on a graph. Initially, each vertex is colored white or black. At each round, each vertex is colored by the color shared by the majority of vertices in its neighborhood. We say that a set of vertices is a dynamic...
These are corrections to the second edition of the book ``Vertex algebras for beginners'', University Lecture Series, 10, American Mathematical Society, Providence, RI, 1998....
May 21, 2024 · I have a vertex 150 skimmer and broke the impeller this morning. I was able to temporarily glue it back together but I think it is a matter of time before it bites the dust. Anyone have …
Dec 2, 2011 · Vertex Puratek 100gph RO/DI mfdrookie516 Mar 10, 2012 None Jump to Last Mar 10, 2012 #1
Mar 23, 2020 · Hey everyone, my vertex 180 skimmer’s impeller recently broke, and I cannot find anywhere a replacement. I understand that they are discontinued, and are...
Feb 24, 2020 · There was a time in the early 2010s when Vertex Aquaristik had an outsize influence on the reef aquarium hobby – their skimmers, reactors and a growing catalog of other reef aquarium …
Oct 1, 2017 · Good morning all and Happy new year! i'm having a little trouble finding replacement parts for my vertex 180i skimmer. i have searched the web, LFS,BRS,Marinedepot, also tried going …
Aug 18, 2017 · I have been using a Vertex Omega 130 on my tank for nearly a year now. If it doesn't start near immediately after applying power check for an obstruction in the pump. It is easily …
Mar 20, 2020 · I've been trying decide on a new protein skimmer for my 125 gallon tank for some time now and yesterday I finally ordered the Vertex Omega 180I. When I placed the order I knew that this …
Oct 7, 2012 · My vertex omega 150 pump impeller has some ceramic that chipped off. I was interested in a replacing the whole pump if possible. Quick search got me the tunze 9420 but I didn't know if …
We show that the vertex-reinforced jump process on the $d$-dimensional lattice with long-range jumps is transient in any dimension $d$ as long as the initial weights do not decay too fast. The main ingredients in the proof are: an analysis of the cor...
In a vertex-colored graph, an edge is happy if its endpoints have the same color. Similarly, a vertex is happy if all its incident edges are happy. Motivated by the computation of homophily in social networks, we consider the algorithmic aspects of t...
In 1935, Pauling estimated the residual entropy of water ice with remarkable accuracy by considering the degeneracy of the ice rule {\it solely at the vertex level}. Indeed, his estimate works well for both the three-dimensional pyrochlore lattice an...
Two vertex colorings of a graph are Kempe equivalent if they can be transformed into each other by a sequence of switchings of two colors of vertices. It is PSPACE-complete to determine whether two given vertex $k$-colorings of a graph are Kempe equi...
Given a graph $G=(V,E)$ and a proper vertex colouring of $G$, a Kempe chain is a subset of $V$ that induces a maximal connected subgraph of $G$ in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from anoth...
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