Related papers: A dichotomy theorem on the complexity of 3-uniform…
Algorithmic extension problems of partial graph representations such as planar graph drawings or geometric intersection representations are of growing interest in topological graph theory and graph drawing. In such an extension problem, we…
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topological structure of hypergraphs embedded in high-dimensional…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Given a plane geometric graph $G$ on $n$ vertices, we want to augment it so that given parity constraints of the vertex degrees are met. In other words, given a subset $R$ of the vertices, we are interested in a plane geometric supergraph…
Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a…
Recently Chase determined the maximum possible number of cliques of size $t$ in a graph on $n$ vertices with given maximum degree. Soon afterward, Chakraborti and Chen answered the version of this question in which we ask that the graph…
In the constraint satisfaction problem ($CSP$), the aim is to find an assignment of values to a set of variables subject to specified constraints. In the minimum cost homomorphism problem ($MinHom$), one is additionally given weights…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
The Nash-Williams conjecture establishes degree sequence conditions ensuring Hamilton cycles in digraphs. An asymptotic version of this conjecture for large digraphs was independently derived by several researchers. We strengthen these…
We study constraint satisfaction problems (CSPs) in the presence of counting quantifiers $\exists^{\geq j}$, asserting the existence of $j$ distinct witnesses for the variable in question. As a continuation of our previous (CSR 2012) paper,…
A packing of two $k$-uniform hypergraphs $H_1$ and $H_2$ is a set $\{H_1', H_2'\}$ of edge-disjoint sub-hypergraphs of the complete $k$-uniform hypergraph $K_n^{(k)}$ such that $H_1'\cong H_1$ and $H_2'\cong H_2$. Whilst the problem of…
The NP-hard general factor problem asks, given a graph and for each vertex a list of integers, whether the graph has a spanning subgraph where each vertex has a degree that belongs to its assigned list. The problem remains NP-hard even if…
Given a graph $G$, the longest path problem asks to compute a simple path of $G$ with the largest number of vertices. This problem is the most natural optimization version of the well known and well studied Hamiltonian path problem, and…
A linearly ordered (LO) $k$-colouring of an $r$-uniform hypergraph assigns an integer from $\{1, \ldots, k \}$ to every vertex so that, in every edge, the (multi)set of colours has a unique maximum. Equivalently, for $r=3$, if two vertices…
Generalizing the notion of split graphs to uniform hypergraphs, we prove that the class of these hypergraphs can be characterized by a finite list of excluded induced subhypergraphs. We show that a characterization by generalized degree…
Boolean-width is a recently introduced graph parameter. Many problems are fixed parameter tractable when parametrized by boolean-width, for instance "Minimum Weighted Dominating Set" (MWDS) problem can be solved in $O^*(2^{3k})$ time given…
For a fixed set ${\cal H}$ of graphs, a graph $G$ is ${\cal H}$-subgraph-free if $G$ does not contain any $H \in {\cal H}$ as a (not necessarily induced) subgraph. A recently proposed framework gives a complete classification on ${\cal…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…
We study unit disk visibility graphs, where the visibility relation between a pair of geometric entities is defined by not only obstacles, but also the distance between them. That is, two entities are not mutually visible if they are too…
For a given $\pi=(\pi_0, \pi_1,..., \pi_k) \in \{0, 1, *\}^{k+1}$, we want to determine whether an input $k$-uniform hypergraph $G=(V, E)$ has a partition $(V_1, V_2)$ of the vertex set so that for all $X \subseteq V$ of size $k$, $X \in E$…