Related papers: Extended formulations for the maximum weighted co-…
We continue the study of graph classes in which the treewidth can only be large due to the presence of a large clique, and, more specifically, of graph classes with bounded tree-independence number. In [Dallard, Milani\v{c}, and…
In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of $H$-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains $NP$-hard for most graphs $H$, we…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
The complexity of the maximum common connected subgraph problem in partial $k$-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial $2$-trees. On the other…
An isomorphism between two graphs is a bijection between their vertices that preserves the edges. We consider the problem of determining whether two finite undirected weighted graphs are isomorphic, and finding an isomorphism relating them…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
We study the maximum induced matching problem on a graph g. Induced matchings correspond to independent sets in L2(g), the square of the line graph of g. The problem is NP-complete on bipartite graphs. In this work, we show that for a…
In this paper, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an…
Let $G=(V,E))$ be a directed graph. A $2$-twinless block in $G$ is a maximal vertex set $B\subseteq V$ of size at least $2$ such that for each pair of distinct vertices $x,y \in B$, and for each vertex $w\in V\setminus\left\lbrace x,y…
We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\delta \cdot…
A proportionally dense subgraph (PDS) of a graph is an induced subgraph of size at least two such that every vertex in the subgraph has proportionally as many neighbors inside as outside of the subgraph. Then, maxPDS is the problem of…
In a bounded max-coloring of a vertex/edge weighted graph, each color class is of cardinality at most $b$ and of weight equal to the weight of the heaviest vertex/edge in this class. The bounded max-vertex/edge-coloring problems ask for…
The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the…
We present a new formulation of the maximum clique problem of a graph in complex space. We start observing that the adjacency matrix A of a graph can always be written in the form A = B B where B is a complex, symmetric matrix formed by…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…
Let $t$ be a positive real number. A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough.…
In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and…
We consider a Bar Charts Packing Problem (BCPP), in which it is necessary to pack bar charts (BCs) in a strip of minimum length. The problem is, on the one hand, a generalization of the Bin Packing Problem (BPP), and, on the other hand, a…
This paper presents a fast and simple new 2-approximation algorithm for minimum weighted vertex cover. The unweighted version of this algorithm is equivalent to a well-known greedy maximal independent set algorithm. We prove that this…
Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…