A 3D bar plot on a flattened surface, showing the population distribution of the United States. This graph is created by flattening a 3D surface of US Map and then plotting the city population as 3D bars on it. The surface is set transparent. Add a 5-column plot to the right as a cr...
In this note the reducts of the Henson graphs with a constant are determined up to first-order interdefinability. It is shown that up to first-order interdefinability (H 3 ,E,0) ( H 3 , E , 0 ) mathContainer Loading Mathjax has 13 reducts and (H n ,E,0) ( H n , E , 0...
Figure 8. Graphs showing the lines crossing the y‐axis. Example 4 Find the slope of x –y = 3 using coordinates. To find the slope of the line, pick any two points on the line, such as A (3, 0) and B (5, 2), and calculate the slope. Example 5 Find the slope of y ...
If we have a speed–time graph showing motion at a constant speed, we know that this will be represented by a horizontal line. For example, consider the graph below. We may pick any point on this line and trace down vertically to the time axis to find the time value associated with a...
We then use these isoperimetric properties to investigate the structure of the giant component in supercritical percolation on these product graphs, that is, when , where d is the degree of the product graph and is a small enough constant. We show that typically has edge-expansion . Further...
There are several plots in NCSS for showing distributions of groups. Dot plots show a single symbol for each point in the group (the points are jittered to help see points that overlap). The density plot shows an estimated density curve based on the concentration of points along the number...
The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of $2^k$ then there must be a periodic point wi...
A graph H is called chromatic-choosable if χ(H)=χ(H). It is an interesting problem to find graphs that are chromatic-choosable. A natural question raised by Xuding Zhu (2013) is whether there exists a constant integer k such that Gk is chromatic-choosable for every graph G. Motivated...
A class of graphs G has bounded clique-width if there is a constant c such that the clique-width of every graph in G is at most c; otherwise the clique-width of G is unbounded. 1.2. Our results We show fixed-parameter tractability results for three problems, namely for Colouring, ...
In fact, the coefficient of |V(H)| in Theorem 2 is not very far from the truth, showing that the bound of Theorem 1 does not extend to G-colorings. Indeed, consider a triangle-free graph H=H(α) such that α(H)=α and has as many vertices as possible — in other words, H ...