Related papers: Feedback Vertex Set and Even Cycle Transversal for…

Let G=(A,B,E) be a bipartite graph with color classes A and B. The graph G is chordal bipartite if G has no induced cycle of length more than four. Let G=(V,E) be a graph. A feedback vertex set F is a set of vertices F subset V such that…

Given a graph $G$, denote by $h(G)$ the smallest size of a subset of $V(G)$ which intersects every maximum independent set of $G$. We prove that any graph $G$ without induced matching of size $t$ satisfies $h(G)\le \omega(G)^{3t-3+o(1)}$.…

\emph{Strictly Chordality-$k$ graphs ($SC_k$)} are graphs which are either cycle-free or every induced cycle is of length exactly $k, k \geq 3$. Strictly chordality-3 and strictly chordality-4 graphs are well known chordal and chordal…

In the \textsc{Subset Feedback Vertex Set (Subset-FVS)} problem the input is a graph $G$, a subset \(T\) of vertices of \(G\) called the `terminal' vertices, and an integer $k$. The task is to determine whether there exists a subset of…

Paths $P_1,\ldots,P_k$ in a graph $G=(V,E)$ are mutually induced if any two distinct $P_i$ and $P_j$ have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to decide if…

The Subset Feedback Vertex Set problem generalizes the classical Feedback Vertex Set problem and asks, for a given undirected graph $G=(V,E)$, a set $S \subseteq V$, and an integer $k$, whether there exists a set $X$ of at most $k$ vertices…

In algorithmic graph theory, a classic open question is to determine the complexity of the Maximum Independent Set problem on $P_t$-free graphs, that is, on graphs not containing any induced path on $t$ vertices. So far, polynomial-time…

A mixed graph is a graph with both directed and undirected edges. We present an algorithm for deciding whether a given mixed graph on $n$ vertices contains a feedback vertex set (FVS) of size at most $k$, in time $2^{O(k)}k! O(n^4)$. This…

The Induced Graph Matching problem asks to find k disjoint induced subgraphs isomorphic to a given graph H in a given graph G such that there are no edges between vertices of different subgraphs. This problem generalizes the classical…

We show that, for every fixed positive integers $r$ and $k$, \textsc{Max-Weight List $r$-Colorable Induced Subgraph} admits a polynomial-time algorithm on $kP_3$-free graphs. This problem is a common generalization of \textsc{Max-Weight…

In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead…

This is my PhD thesis which was defended in May 2021. We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications.…

We study the Independent Set (IS) problem in $H$-free graphs, i.e., graphs excluding some fixed graph $H$ as an induced subgraph. We prove several inapproximability results both for polynomial-time and parameterized algorithms.…

We study Steiner Forest on $H$-subgraph-free graphs, that is, graphs that do not contain some fixed graph $H$ as a (not necessarily induced) subgraph. We are motivated by a recent framework that completely characterizes the complexity of…

A graph is $H$-free if it does not contain an induced subgraph isomorphic to $H$. We denote by $P_k$ and $C_k$ the path and the cycle on $k$ vertices, respectively. In this paper, we prove that 4-COLORING is NP-complete for $P_7$-free…

For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…

The Subset Feedback Vertex Set problem (SFVS), to delete $k$ vertices from a given graph such that any vertex in a vertex subset (called a terminal set) is not in a cycle in the remaining graph, generalizes the famous Feedback Vertex Set…

In this paper we consider Simultaneous Feedback Edge Set (Sim-FES) problem. In this problem, the input is an $n$-vertex graph $G$, an integer $k$ and a coloring function ${\sf col}: E(G) \rightarrow 2^{[\alpha]}$ and the objective is to…

Feedback Vertex Set is a classic combinatorial optimization problem that asks for a minimum set of vertices in a given graph whose deletion makes the graph acyclic. From the point of view of parameterized algorithms and fixed-parameter…

The complexity of {\sc Colouring} is fully understood for $H$-free graphs, but there are still major complexity gaps if two induced subgraphs $H_1$ and $H_2$ are forbidden. Let $H_1$ be the $s$-vertex cycle $C_s$ and $H_2$ be the $t$-vertex…