Related papers: Independent sets and hitting sets of bicolored rec…
We study two-stage bipartite matching, in which the edges of a bipartite graph on vertices $(B_1 \cup B_2, I)$ are revealed in two batches. In stage one, a matching must be selected from among revealed edges $E \subseteq B_1 \times I$. In…
Biclustering, also called co-clustering, block clustering, or two-way clustering, involves the simultaneous clustering of both the rows and columns of a data matrix into distinct groups, such that the rows and columns within a group display…
Given a proper edge-coloring of a loopless multigraph, the palette of a vertex is defined as the set of colors of the edges which are incident with it. The palette index of a multigraph is defined as the minimum number of distinct palettes…
We present a method for learning max-weight matching predictors in bipartite graphs. The method consists of performing maximum a posteriori estimation in exponential families with sufficient statistics that encode permutations and data…
In this paper we study the minimal size of edges in hypergraph families that guarantees the existence of a polychromatic coloring, that is, a $k$-coloring of a vertex set such that every hyperedge contains a vertex of all $k$ color classes.…
Given a hypergraph $H = (V,E)$, what is the smallest subset $X \subseteq V$ such that $e \cap X \neq \emptyset$ holds for all $e \in E$? This problem, known as the hitting set problem, is a basic problem in parameterized complexity theory.…
The maximum independent set problem is one of the most important problems in graph algorithms and has been extensively studied in the line of research on the worst-case analysis of exact algorithms for NP-hard problems. In the weighted…
Let $R$ and $B$ be two disjoint sets of points in the plane where the points of $R$ are colored red and the points of $B$ are colored blue, and let $n=|R\cup B|$. A bichromatic spanning tree is a spanning tree in the complete bipartite…
We establish a theorem regarding the maximum size of an {\it{induced}} matching in the bipartite complement of the incidence graph of a set system $(X,\mathcal{F})$. We show that this quantity plus one provides an upper bound on the…
Given a universe $\mathcal{U}=R \cup B$ of a finite set of red elements $R$, and a finite set of blue elements $B$ and a family $\mathcal{F}$ of subsets of $\mathcal{U}$, the \RBSC problem is to find a subset $\mathcal{F}'$ of $\mathcal{F}$…
An independent set in a graph is a set of pairwise non-adjacent vertices, and alpha(G) is the size of a maximum independent set in the graph G. A matching is a set of non-incident edges, while mu(G) is the cardinality of a maximum matching.…
Bin Packing with Minimum Color Fragmentation (BPMCF) is an extension of the Bin Packing Problem in which each item has a size and a color and the goal is to minimize the sum of the number of bins containing items of each color. In this…
In this paper we obtain some upper bounds for $b$-chromatic number of $K_{1,t}$ -free graphs, graphs with given minimum clique partition and bipartite graphs. These bounds are in terms of either clique number or chromatic number of graphs…
In 2020, we initiated a systematic study of graph classes in which the treewidth can only be large due to the presence of a large clique, which we call $(\mathrm{tw},\omega)$-bounded. While $(\mathrm{tw},\omega)$-bounded graph classes are…
A matching of a graph is a subset of edges no two of which share a common vertex, and a maximum matching is a matching of maximum cardinality. In a $b$-matching every vertex $v$ has an associated bound $b_v$, and a maximum $b$-matching is a…
A conflict-free coloring of a graph $G$ is a (partial) coloring of its vertices such that every vertex $u$ has a neighbor whose assigned color is unique in the neighborhood of $u$. There are two variants of this coloring, one defined using…
Proper conflict-free coloring is an intermediate notion between proper coloring of a graph and proper coloring of its square. It is a proper coloring such that for every non-isolated vertex, there exists a color appearing exactly once in…
A matching $M$ in a graph $G$ is said to be uniquely restricted if there is no other matching in $G$ that matches the same set of vertices as $M$. We describe a polynomial-time algorithm to compute a maximum cardinality uniquely restricted…
Geometric hitting set problems, in which we seek a smallest set of points that collectively hit a given set of ranges, are ubiquitous in computational geometry. Most often, the set is discrete and is given explicitly. We propose new…
The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size $k$, when $k$ is part of the…