Related papers: Extremal aspects of graph and hypergraph decomposi…
Developing further Stein's recent notion of relative end degrees in infinite graphs, we investigate which degree assumptions can force a locally finite graph to contain a given finite minor, or a finite subgraph of given minimum degree.…
Building on existing algorithms and results, we offer new insights and algorithms for various problems related to detecting maximal and maximum bicliques. Most of these results focus on graphs with small maximum degree, providing improved…
As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion…
Given graphs $G$ and $H$, we consider the problem of decomposing a properly edge-colored graph $G$ into few parts consisting of rainbow copies of $H$ and single edges. We establish a close relation to the previously studied problem of…
Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of…
Constraint Satisfaction Problems (CSPs) play a central role in many applications in Artificial Intelligence and Operations Research. In general, solving CSPs is NP-complete. The structure of CSPs is best described by hypergraphs. Therefore,…
This is a survey of old and new problems and results in additive number theory.
We consider the problem of minimizing the number of triangles in a graph of given order and size and describe the asymptotic structure of extremal graphs. This is achieved by characterizing the set of flag algebra homomorphisms that…
This article emphasizes an extension of the study of metric and par- tition dimension to hypergraphs. We give a sharp lower bounds for the metric and partition dimension of hypergraphs in general and give exact values under specified…
In recent years, significant advances have been made in the design and evaluation of balanced (hyper)graph partitioning algorithms. We survey trends of the last decade in practical algorithms for balanced (hyper)graph partitioning together…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
In recent years several classical results in extremal graph theory have been improved in a uniform way and their proofs have been simplified and streamlined. These results include a new Erd\H{o}s-Stone-Bollob\'as theorem, several stability…
In this paper we discuss reconstruction problems for graphs. We develop some new ideas like isomorphic extension of isomorphic graphs, partitioning of vertex sets into sets of equivalent points, subdeck property, etc. and develop an…
This paper considers the degree-diameter problem for undirected circulant graphs. The focus is on extremal graphs of given (small) degree and arbitrary diameter. The published literature only covers graphs of up to degree 7. The approach…
Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected…
Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…
We give some illustrative applications of our recent result on decompositions of labelled complexes, including some new results on decompositions of hypergraphs with coloured or directed edges. For example, we give fairly general conditions…
A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…
Extremal problems involving independent sets are much studied. Two of the most important extremal problems in this context are concerned with the sharp upper bounds for the number of independent sets of fixed size and the independence…