相关论文: Research problem: The completion number of a graph
The domatic number of a graph is the maximum number of vertex disjoint dominating sets that partition the vertex set of the graph. In this paper we consider the fractional variant of this notion. Graphs with fractional domatic number 1 are…
The set of semialgebraic graphs having countable list-chromatic numbers is characterized. Some other related sets of graphs having countable list-chromatic numbers also are.
We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the…
The total graph is built by joining the graph to its line graph by means of the incidences. We introduce a similar construction for signed graphs. Under two similar definitions of the line signed graph, we define the corresponding total…
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…
For a class $\mathcal{G}$ of graphs, the objective of \textsc{Subgraph Complementation to} $\mathcal{G}$ is to find whether there exists a subset $S$ of vertices of the input graph $G$ such that modifying $G$ by complementing the subgraph…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.
In this paper, we mainly study the trace norm of the adjacency matrix of a graph, also known as the energy of graph. We give the maximum trace norms for the graph and its complement. In fact, the above problem is stated and solved in a more…
Counting maximum matchings in a graph is of great interest in statistical mechanics, solid-state chemistry, theoretical computer science, mathematics, among other disciplines. However, it is a challengeable problem to explicitly determine…
A total dominator coloring of a graph $G$ is a proper coloring of $G$ in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number of a graph is the minimum number of color classes…
This is a contribution to the number theory of the dimer problem. The number of dimer coverings (i.e., perfect matchings) of a square lattice graph is discussed modulo powers of 2.
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
In this paper, structural properties of chordal graphs are analysed, in order to establish a relationship between these structures and integer Laplacian eigenvalues. We present the characterization of chordal graphs with equal vertex and…
Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…
We introduce a new -as far as we know- problem, according to which we are asked to match sequences of two digits in matrices having entries among those two digits (but others too) and prove that this problem is NP-complete