Now showing items 1-20 of 23

• #### A (2 + ε)-Factor Approximation Algorithm for Split Vertex Deletion ﻿

(Journal article; Peer reviewed, 2020)
In the Split Vertex Deletion (SVD) problem, the input is an n-vertex undirected graph G and a weight function w: V(G) → ℕ, and the objective is to find a minimum weight subset S of vertices such that G-S is a split graph ...
• #### b-Coloring Parameterized by Clique-Width ﻿

(Journal article; Peer reviewed, 2021)
We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial-time results on graph classes, and answers open questions posed by ...
• #### Balanced judicious bipartition is fixed-parameter tractable ﻿

(Journal article; Peer reviewed, 2019)
The family of judicious partitioning problems, introduced by Bollobás and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of ...
• #### Bidimensionality and Kernels ﻿

(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, ...
• #### Bisection of Bounded Treewidth Graphs by Convolutions ﻿

(Journal article; Peer reviewed, 2019)
In the Bisection problem, we are given as input an edge-weighted graph G. The task is to find a partition of V(G) into two parts A and B such that ||A| - |B|| <= 1 and the sum of the weights of the edges with one endpoint ...
• #### Covering Vectors by Spaces in Perturbed Graphic Matroids and Their Duals ﻿

(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 ﻿

(Peer reviewed; Journal article, 2019)
• #### ETH-tight algorithms for long path and cycle on unit disk graphs ﻿

(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 ...
• #### Fault tolerant subgraphs with applications in kernelization ﻿

(Journal article; Peer reviewed, 2020)
In the past decade, the design of fault tolerant data structures for networks has become a central topic of research. Particular attention has been given to the construction of a subgraph H of a given digraph D with as ...

(2005)
• #### Going Far from Degeneracy ﻿

(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 ﻿

(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 ﻿

(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 ...
• #### On cutwidth parameterized by vertex cover ﻿

(Peer reviewed; Journal article, 2014-04)
We study the CUTWIDTH problem, where the input is a graph G, and the objective is find a linear layout of the vertices that minimizes the maximum number of edges intersected by any vertical line inserted between two ...
• #### Packing cycles faster than Erdos-Posa ﻿

(Journal article; Peer reviewed, 2019)
The Cycle Packing problem asks whether a given undirected graph $G=(V,E)$ contains $k$ vertex-disjoint cycles. Since the publication of the classic Erdös--Pósa theorem in 1965, this problem received significant attention ...
• #### Parameterization Above a Multiplicative Guarantee ﻿

(Journal article; Peer reviewed, 2020)
Parameterization above a guarantee is a successful paradigm in Parameterized Complexity. To the best of our knowledge, all fixed-parameter tractable problems in this paradigm share an additive form defined as follows. Given ...
• #### The Parameterized Complexity of Guarding Almost Convex Polygons ﻿

(Journal article; Peer reviewed, 2020)
The Art Gallery problem is a fundamental visibility problem in Computational Geometry. The input consists of a simple polygon P, (possibly infinite) sets G and C of points within P, and an integer k; the task is to decide ...
• #### Parameterized Single-Exponential Time Polynomial Space Algorithm for Steiner Tree ﻿

(Peer reviewed; Journal article, 2019)
In the Steiner Tree problem, we are given as input a connected $n$-vertex graph with edge weights in $\{1,2,\ldots,W\}$, and a set of $k$ terminal vertices. Our task is to compute a minimum-weight tree that contains ...
• #### Path contraction faster than $2^n$ ﻿

(Journal article; Peer reviewed, 2020)
A graph $G$ is contractible to a graph $H$ if there is a set $X \subseteq E(G)$, such that $G/X$ is isomorphic to $H$. Here, $G/X$ is the graph obtained from $G$ by contracting all the edges in $X$. For a family of graphs ...
• #### Path Contraction Faster Than 2n ﻿

(Peer reviewed; Journal article, 2019)
A graph G is contractible to a graph H if there is a set X subseteq E(G), such that G/X is isomorphic to H. Here, G/X is the graph obtained from G by contracting all the edges in X. For a family of graphs F, the F-Contraction ...