In the paper we state and prove theorem describing the upper bound on number of the graphs that have fixed number of vertices |V| and can be colored with the fixed number of n colors. The bound relates both numbers using power of 2, while the exponent is the difference between |V| ...
On the Structure of Graphs with Bounded Asteroidal Number A set A⊆V of the vertices of a graph G=(V,E) is an asteroidal set if for each vertex a∈A, the set A\\{a} is contained in one component of G−N[a]. Th... T Kloks,D Kratsch,H Müller - 《Graphs & Combinatori...
The article discusses the study on the independence number of distance graphs with vertices in {1, 0, 1} n wherein only one linear-algebraic method was known to be effective in obtaining the upper bounds of vertices. It notes that the authors have developed a techni...
All the work made so far on edge-covering a graph by cliques focus on finding the minimum number of cliques that cover the graph. On this paper, we fix the number of cliques that cover a graph by the same number of vertices that the graph has, and give an upper bound for the sum ...
We want to derive a linear in (n−k) bound on the number of edges in a graph that does not contain (k+1)-connected subgraphs. But the bound becomes linear only for graphs with large number of vertices; while for small graphs the dependency is quadratic in n−k. The main difficult...
The number of graphs and a random graph with a given degree sequence We consider the set of all graphs on n labeled vertices with prescribed degrees D=(d_1, ..., d_n). For a wide class of tame degree sequences D we prove a c... A Barvinok,JA Hartigan - 《Random Structures & ...
Here, the distance between two distinct vertices s and t is defined as the length (i.e., the number of edges) of a shortest s-t path. A path of length at most l is referred to as an l-hop path. There are many studies on graphs with high edge-connectivity and ones with small ...
We show that the number of perfect matching in a simple graph $G$ with an even number of vertices and degree sequence $d_1,d_2, ..., d_n$ is at most $\\prod_{i=1}^n (d_i !)^{\\frac{1}{2d_i}}$. This bound is sharp if and only if $G$ is a union of complete ...
time algorithm for deciding the divergence or convergence of a graph. In this work we prove that any graph with at least 7 bicliques diverges under the biclique operator. Furthermore, we prove that graphs with no twin vertices that are not divergent have at most 12 vertices, which leads to...
For a given choice of integer parameters 4 <= k <= n, the purpose of this program is to list all simple graphs on n vertices with no isolated vertices that are edge-k-critical, meaning that the graph has chromatic number k and the removal of any edge from the graph results in a gr...