An undirected graph is said to be split if its vertex set can be partitioned into two sets such that the subgraph induced on one of them is a complete graph and the subgraph induced on the other isâ€¦ (More)

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, asâ€¦ (More)

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutionsâ€¦ (More)

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditionalâ€¦ (More)

We address the parameterized complexity of Max Colorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis andâ€¦ (More)

Let M = (E, I) be a matroid. A k-truncation of M is a matroid M â€² = (E, I ) such that for any A âŠ† E, A âˆˆ Iâ€² if and only if |A| â‰¤ k and A âˆˆ I. Given a linear representation of M we consider theâ€¦ (More)

Let <i>M</i>=(<i>E</i>, <i>I</i>) be a matroid and let <i>S</i>={<i>S</i><sub>1</sub>, ċ , <i>S</i><sub>t</sub>} be a family of subsets of <i>E</i> of size <i>p</i>.â€¦ (More)

For fixed integers r, ` â‰¥ 0, a graph G is called an (r, `)-graph if the vertex set V (G) can be partitioned into r independent sets and ` cliques. This brings us to the following naturalâ€¦ (More)

Given a universe U := U1]Â· Â· Â·]Ur, and a r-uniform family F âŠ† U1Ã—Â· Â· Â·Ã—Ur, the r-dimensional matching problem asks if F admits a collection of k mutually disjoint sets. The special case when r = 3 isâ€¦ (More)