Related papers: An efficient algorithm for $\mathcal{F}$-subgraph-…

We prove that every $n$-vertex $K_t$-minor-free graph $G$ of maximum degree $\Delta$ has a set $F$ of $O(t^2(\log t)^{1/4}\sqrt{\Delta n})$ edges such that every component of $G - F$ has at most $n/2$ vertices. This is best possible up to…

We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…

In the Disjoint Paths problem, the input is an undirected graph $G$ on $n$ vertices and a set of $k$ vertex pairs, $\{s_i,t_i\}_{i=1}^k$, and the task is to find $k$ pairwise vertex-disjoint paths connecting $s_i$ to $t_i$. The problem was…

We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…

In the Online Delayed Connected H-Node-Deletion Problem, an unweighted graph is revealed vertex by vertex and it must remain free of any induced copies of a specific connected induced forbidden subgraph H at each point in time. To achieve…

We consider the embeddability problem of a graph G into a two-dimensional simplicial complex C: Given G and C, decide whether G admits a topological embedding into C. The problem is NP-hard, even in the restricted case where C is…

A graph is called (claw,diamond)-free if it contains neither a claw (a $K_{1,3}$) nor a diamond (a $K_4$ with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of…

For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. This brings us to the following natural parameterized questions:…

Bidimensionality is the most common technique to design subexponential-time parameterized algorithms on special classes of graphs, particularly planar graphs. The core engine behind it is a combinatorial lemma of Robertson, Seymour and…

We extend our previous algorithm that generates all labeled graphs with a given graphical degree sequence to generate all labeled triangle-free graphs with a given graphical degree sequence. The algorithm uses various pruning techniques to…

The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…

The $k$-vertex disjoint paths problem is one of the most studied problems in algorithmic graph theory. In 1994, Schrijver proved that the problem can be solved in polynomial time for every fixed $k$ when restricted to the class of planar…

The \textsc{Bipartite Contraction} problem is to decide, given a graph $G$ and a parameter $k$, whether we can can obtain a bipartite graph from $G$ by at most $k$ edge contractions. The fixed-parameter tractability of the problem was shown…

It is known that problems like Vertex Cover, Feedback Vertex Set and Odd Cycle Transversal are polynomial time solvable in the class of chordal graphs. We consider these problems in a graph that has at most $k$ vertices whose deletion…

A dominating induced matching, also called an efficient edge domination, of a graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F \subseteq E$ of edges in the graph such that no two edges in $F$ share a common endpoint…

The \emph{Product Structure Theorem} for planar graphs (Dujmovi\'c et al.\ \emph{JACM}, \textbf{67}(4):22) states that any planar graph is contained in the strong product of a planar $3$-tree, a path, and a $3$-cycle. We give a simple…

For a set of graphs $\mathcal{H}$, the \textsc{$\mathcal{H}$-free Edge Deletion} problem asks to find whether there exist at most $k$ edges in the input graph whose deletion results in a graph without any induced copy of $H\in\mathcal{H}$.…

Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed…

For an undirected graph G, we consider the following problems: given a fixed graph H, can we partition the vertices of G into two non-empty sets A and B such that neither the induced graph G[A] nor G[B] contain H (i) as a subgraph? (ii) as…

A 2-club is a graph of diameter at most two. In the decision version of the parametrized {\sc 2-Club Cluster Edge Deletion} problem, an undirected graph $G$ is given along with an integer $k\geq 0$ as parameter, and the question is whether…