Related papers: Two extremal problems in the light of Lex graphs
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
One powerful method for upper-bounding the largest independent set in a graph is the Hoffman bound, which gives an upper bound on the largest independent set of a graph in terms of its eigenvalues. It is easily seen that the Hoffman bound…
This note answers extremal questions like: what is the maximum number of edges in a graph of order n, which belongs to some hereditary property. The same question is answered also for the spectral radius and other similar parameters.
This paper studies $k$-claw-free graphs, exploring the connection between an extremal combinatorics question and the power of a convex program in approximating the maximum-weight independent set in this graph class. For the extremal…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
On 12 February 2020 the Royal Statistical Society hosted a meeting to discuss the forthcoming paper ``Graphical models for extremes'' by Sebastian Engelke and Adrien Hitz [arXiv:1812.01734]. This short note is a supplement to my discussion…
We study the problems of bounding the number weak and strong independent sets in $r$-uniform, $d$-regular, $n$-vertex linear hypergraphs with no cross-edges. In the case of weak independent sets, we provide an upper bound that is tight up…
We use an entropy based method to study two graph maximization problems. We upper bound the number of matchings of fixed size $\ell$ in a $d$-regular graph on $N$ vertices. For $\frac{2\ell}{N}$ bounded away from 0 and 1, the logarithm of…
We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-known Hoffman-type bound.
For a simple graph $F$, let $\mathrm{EX}(n, F)$ and $\mathrm{EX_{sp}}(n,F)$ be the set of graphs with the maximum number of edges and the set of graphs with the maximum spectral radius in an $n$-vertex graph without any copy of the graph…
A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the…
We characterize the connected graphs of given order $n$ and given independence number $\alpha$ that maximize the number of maximum independent sets. For $3\leq \alpha\leq n/2$, there is a unique such graph that arises from the disjoint…
In the literature, several different identification problems in graphs have been studied, the most widely studied such problems are the ones based on dominating sets as a tool of identification. Hereby, the objective is to separate any two…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
A set of graphs is said to be independent if there is no homomorphism between distinct graphs from the set. We consider the existence problems related to the independent sets of countable graphs. While the maximal size of an independent set…
The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation…
Counting independent sets in graphs and hypergraphs under a variety of restrictions is a classical question with a long history. It is the subject of the celebrated container method which found numerous spectacular applications over the…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
We study the following inverse graph-theoretic problem: how many vertices should a graph have given that it has a specified value of some parameter. We obtain asymptotic for the minimal number of vertices of the graph with the given number…
We survey various aspects of infinite extremal graph theory and prove several new results. The lead role play the parameters connectivity and degree. This includes the end degree. Many open problems are suggested.