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 ...

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 ...

A tournament is a directed graph in which there is a single arc between every pair of distinct vertices. Given a tournament T on n vertices, we explore the classical and parameterized complexity of the problems of determining ...

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 ...

An input to a conflict-free variant of a classical problem Gamma, called Conflict-Free Gamma, consists of an instance I of Gamma coupled with a graph H, called the conflict graph. A solution to Conflict-Free Gamma in (I,H) ...

We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance ...

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 ...

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 ...

For a fixed graph H, the H-free Edge Editing problem asks whether we can modify a given graph G by adding or deleting at most k edges such that the resulting graph does not contain H as an induced subgraph. The problem is ...

In this paper we study two classical cut problems, namely Multicut and Multiway Cut on chordal graphs and split graphs. In the Multicut problem, the input is a graph G, a collection of 𝓁 vertex pairs (si, ti), i ∈ [𝓁], ...