9 papers
Rainbow Arborescence Conjecture
Kristóf Bérczi, Tamás Király, Yutaro Yamaguchi +1
The famous Ryser--Brualdi--Stein conjecture asserts that every Latin square contains a partial transversal of size . Since its appearance, the conjecture has attr…
A new approach to bipartite stable matching optimization
Tamás Fleiner, András Frank, Tamás Király
As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for comp…
The NTU Partitioned Matching Game for International Kidney Exchange Programs
Gergely Csáji, Tamás Király, Zsuzsa Mészáros-Karkus
Motivated by the real-world problem of international kidney exchange (IKEP), recent literature introduced a generalized transferable utility matching game featuring a partition of…
Popular Maximum-Utility Matchings with Matroid Constraints
Gergely Csáji, Tamás Király, Kenjiro Takazawa +1
We investigate weighted settings of popular matching problems with matroid constraints. The concept of popularity was originally defined for matchings in bipartite graphs, where ve…
Finding Spanning Trees with Perfect Matchings
Kristóf Bérczi, Tamás Király, Yusuke Kobayashi +2
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem:…
Multiway Cuts with a Choice of Representatives
Kristóf Bérczi, Tamás Király, Daniel P. Szabo
In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} . In this…
Matroid Intersection under Minimum Rank Oracle
Mihály Bárász, Kristóf Bérczi, Tamás Király +3
In this paper, we consider the tractability of the matroid intersection problem under the minimum rank oracle. In this model, we are given an oracle that takes as its input a set o…
Hypergraph Connectivity Augmentation in Strongly Polynomial Time
Kristóf Bérczi, Karthekeyan Chandrasekaran, Tamás Király +1
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where…
Splitting-off in Hypergraphs
Kristóf Bérczi, Karthekeyan Chandrasekaran, Tamás Király +1
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of…