• An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOL 

      Fomin, Fedor; Golovach, Petr; Stamoulis, Giannos; Thilikos, Dimitrios M. (Journal article; Peer reviewed, 2020)
      In general, a graph modification problem is defined by a graph modification operation ⊠ and a target graph property 𝒫. Typically, the modification operation ⊠ may be vertex removal, edge removal, edge contraction, or edge ...
    • Approximating Acyclicity Parameters of Sparse Hypergraphs 

      Fomin, Fedor; Golovach, Petr; Thilikos, Dimitrios (Conference object; Peer reviewed; Journal article, 2009)
      The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello (PODS'99, PODS'01) in order to extend the concept of hypergraph acyclicity. These notions were further generalized ...
    • Bidimensionality and Kernels 

      Fomin, Fedor; Lokshtanov, Daniel; Saurabh, Saket; Thilikos, Dimitrios (Journal article; Peer reviewed, 2020)
      Bidimensionality theory was introduced by [E. D. Demaine et al., J. ACM, 52 (2005), pp. 866--893] as a tool to obtain subexponential time parameterized algorithms on H-minor-free graphs. In [E. D. Demaine and M. Hajiaghayi, ...
    • Building large k-cores from sparse graphs 

      Fomin, Fedor; Sagunov, Danil; Simonov, Kirill (Journal article; Peer reviewed, 2020)
      A popular model to measure network stability is the k-core, that is the maximal induced subgraph in which every vertex has degree at least k. For example, k-cores are commonly used to model the unraveling phenomena in ...
    • Connecting Vertices by Independent Trees 

      Basavaraju, Manu; Fomin, Fedor; Golovach, Petr; Saurabh, Saket (Conference object, 2014)
      We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T1, . . . , Ts of G are completely independent spanning trees of U if each of them contains U , and ...
    • Covering Vectors by Spaces in Perturbed Graphic Matroids and Their Duals 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019)
      Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, an r-rank perturbed graphic matroid M is a binary matroid that can be represented ...
    • Decomposition of map graphs with applications 

      Fomin, Fedor; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019)
    • Diverse Collections in Matroids and Graphs 

      Fomin, Fedor; Golovach, Petr; Panolan, Fahad; Philip, Geevarghese; Saurabh, Saket (Journal article; Peer reviewed, 2021)
      We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems, two from the theory of matroids and the third from graph theory. The input to the Weighted Diverse ...
    • Diverse Pairs of Matchings 

      Fomin, Fedor; Golovach, Petr; Jaffke, Lars; Philip, Geevarghese; Sagunov, Danil (Journal article; Peer reviewed, 2020)
      We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse ...
    • ETH Tight Algorithms for Geometric Intersection Graphs: Now in Polynomial Space 

      Fomin, Fedor; Golovach, Petr; Inamdar, Tanmay Nitin; Saurabh, Saket (Journal article; Peer reviewed, 2021)
      De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted ...
    • ETH-tight algorithms for long path and cycle on unit disk graphs 

      Fomin, Fedor; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)
      We present an algorithm for the extensively studied Long Path and Long Cycle problems on unit disk graphs that runs in time 2O(√k)(n + m). Under the Exponential Time Hypothesis, Long Path and Long Cycle on unit disk graphs ...
    • Exact algorithms for treewidth and minimum fill-in 

      Fomin, Fedor; Todinca, Ioan; Kratsch, Dieter; Villanger, Yngve (Journal article, 2006)
    • Exploring Subexponential Parameterized Complexity of Completion Problems 

      Drange, Pål Grønås; Fomin, Fedor; Pilipczuk, Michal Pawel; Villanger, Yngve (Peer reviewed; Journal article, 2014-02-19)
      Let F be a family of graphs. In the F-Completion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k edges can be added to G so that the resulting graph does not contain a graph ...
    • Finding Induced Subgraphs via Minimal Triangulations 

      Fomin, Fedor; Villanger, Yngve (Conference object; Peer reviewed; Journal article, 2010)
      Potential maximal cliques and minimal separators are combinatorial objects which were introduced and studied in the realm of minimal triangulation problems in- cluding Minimum Fill-in and Treewidth. We discover unexpected ...
    • A Fixed-Parameter Perspective on #BIS 

      Curticapean, Radu; Dell, Holger; Fomin, Fedor; Goldberg, Leslie Ann; Lapinskas, John (Peer reviewed; Journal article, 2019-07-18)
      The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RHΠ1. It is believed that #BIS ...
    • Going Far from Degeneracy 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Journal article; Peer reviewed, 2020)
      An undirected graph $G$ is $d$-degenerate if every subgraph of $G$ has a vertex of degree at most $d$. By the classical theorem of Erdös and Gallai from 1959, every graph of degeneracy $d>1$ contains a cycle of length at ...
    • Going Far From Degeneracy 

      Fomin, Fedor; Golovach, Petr; Lokshtanov, Daniel; Panolan, Fahad; Saurabh, Saket; Zehavi, Meirav (Peer reviewed; Journal article, 2019-09-06)
      An undirected graph G is d-degenerate if every subgraph of G has a vertex of degree at most d. By the classical theorem of Erd\H{o}s and Gallai from 1959, every graph of degeneracy d>1 contains a cycle of length at least ...
    • Kernel(s) for Problems with No Kernel: On Out-Trees with Many Leaves 

      Fernau, Henning; Fomin, Fedor; Lokshtanov, Daniel; Raible, Daniel; Saurabh, Saket; Villanger, Yngve (Conference object; Peer reviewed; Journal article, 2009)
      The {\sc \(k\)-Leaf Out-Branching} problem is to find an out-branching, that is a rooted oriented spanning tree, with at least \(k\) leaves in a given digraph. The problem has recently received much attention from the ...
    • Kernelization of Graph Hamiltonicity: Proper H-Graphs 

      Chaplick, Steven; Fomin, Fedor; Golovach, Petr; Knop, Dusan; Zeman, Peter (Journal article; Peer reviewed, 2021)
      We obtain new polynomial kernels and compression algorithms for Path Cover and Cycle Cover, the well-known generalizations of the classical Hamiltonian Path and Hamiltonian Cycle problems. Our choice of parameterization ...
    • Kernelization of Whitney Switches 

      Fomin, Fedor; Golovach, Petr (Journal article; Peer reviewed, 2020)
      A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations ...