Related papers: Connected covering numbers
In this paper we characterize the unique graph whose algebraic connectivity is minimum among all connected graphs with given order and fixed matching number or edge covering number, and present two lower bounds for the algebraic…
Graph theoretical ideas are highly utilized by computer science fields especially data mining. In this field, a data structure can be designed in the form of tree. Covering is a widely used form of data representation in data mining and…
Connected Vertex Cover is one of the classical problems of computer science, already mentioned in the monograph of Garey and Johnson. Although the optimization and decision variants of finding connected vertex covers of minimum size or…
Las Vergnas and Hamidoune studied the number of circuits needed to determine an oriented matroid. In this paper we investigate this problem and some new variants, as well as their interpretation in particular classes of matroids. We present…
Let $ G=(V,E) $ be a simple graph of order $ n $ and size $ m $. A connected edge cover set of a graph is a subset $S$ of edges such that every vertex of the graph is incident to at least one edge of $S$ and the subgraph induced by $S$ is…
Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maximum orbit size (under the action of the matroid automorphism…
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.
Given a graph $G$, the Connected Vertex Cover problem (CVC) asks to find a minimum cardinality vertex cover of $G$ that induces a connected subgraph. In this paper we describe some approaches to solve the CVC problem exactly. First, we give…
The vertex cover number of a graph is the minimum number of vertices that are needed to cover all edges. When those vertices are further required to induce a connected subgraph, the corresponding number is called the connected vertex cover…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We characterise the structure of those graphs of a given order which maximise the number of connected induced subgraphs for seven different graph classes, each with other prescribed parameters like minimum degree, independence number,…
We introduce a notion of connected perimeter for planar sets defined as the lower semi-continuous envelope of perimeters of approximating sets which are measure-theoretically connected. A companion notion of simply connected perimeter is…
Let $G=(V,E)$ be a simple connected graph. A connected edge cover of $G$ is a subset $S\subseteq E$ such that every vertex of $G$ is incident with at least one edge in $S$ and the subgraph induced by $S$ is connected. The connected edge…
We introduce several new concepts about graphs and investigate their basic properties. A longest path in a graph is called a detour and a longest cycle is called a cummerbund. The detour covering number of a graph is the number of vertices…
The proper connection number $pc(G)$ of a connected graph $G$ is defined as the minimum number of colors needed to color its edges, so that every pair of distinct vertices of $G$ is connected by at least one path in $G$ such that no two…
In this article we determine five previously unknown covering array numbers (CANs). We do so using properties of so called balanced covering arrays together with a computational result for these. The balance properties allow us to…
A $(v,k,t)$ {\em covering design}, or {\em covering}, is a family of $k$-subsets, called blocks, chosen from a $v$-set, such that each $t$-subset is contained in at least one of the blocks. The number of blocks is the covering's {\em size},…
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…
Given an undirected simple graph, a subset of the vertices of the graph is a {\em dominating set} if every vertex not in the subset is adjacent to at least one vertex in the subset. A subset of the vertices of the graph is a {\em connected…
A connected set in a graph is a subset of vertices whose induced subgraph is connected. Although counting the number of connected sets in a graph is generally a \#P-complete problem, it remains an active area of research. In 2020, Vince…