Related papers: Parameterized Algorithms for Min-Max Multiway Cut …

$H$-Packing is the problem of finding a maximum number of vertex-disjoint copies of $H$ in a given graph $G$. $H$-Partition is the special case of finding a set of vertex-disjoint copies that cover each vertex of $G$ exactly once. Our goal…

We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…

Most state-of-the-art motion segmentation algorithms draw their potential from modeling motion differences of local entities such as point trajectories in terms of pairwise potentials in graphical models. Inference in instances of minimum…

For graphs $G,H$, a homomorphism from $G$ to $H$ is an edge-preserving mapping from $V(G)$ to $V(H)$. In the list homomorphism problem, denoted by \textsc{LHom}($H$), we are given a graph $G$ and lists $L: V(G) \to 2^{V(H)}$, and we ask for…

We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…

An $h$-queue layout of a graph $G$ consists of a linear order of its vertices and a partition of its edges into $h$ queues, such that no two independent edges of the same queue nest. The minimum $h$ such that $G$ admits an $h$-queue layout…

The generic homomorphism problem, which asks whether an input graph $G$ admits a homomorphism into a fixed target graph $H$, has been widely studied in the literature. In this article, we provide a fine-grained complexity classification of…

Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter clique-width, Hamiltonian Cycle becomes…

We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a $…

Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…

The following optimization problem was introduced in \cite{gutinDAM}, where it was motivated by a real-world problem in defence logistics. Suppose we are given a pair of digraphs $D,H$ and a positive cost $c_i(u)$ for each $u\in V(D)$ and…

A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of…

In the problem (Unweighted) Max-Cut we are given a graph $G = (V,E)$ and asked for a set $S \subseteq V$ such that the number of edges from $S$ to $V \setminus S$ is maximal. In this paper we consider an even harder problem: (Weighted)…

We prove that Graph Isomorphism and Canonization in graphs excluding a fixed graph $H$ as a minor can be solved by an algorithm working in time $f(H)\cdot n^{O(1)}$, where $f$ is some function. In other words, we show that these problems…

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

In the NP-hard Max $c$-Cut problem, one is given an undirected edge-weighted graph $G$ and aims to color the vertices of $G$ with $c$ colors such that the total weight of edges with distinctly colored endpoints is maximal. The case with…

In this paper, we study the Maximum Common Vertex Subgraph problem: Given two input graphs $G_1,G_2$ and a non-negative integer $h$, is there a common subgraph $H$ on at least $h$ vertices such that there is no isolated vertex in $H$. In…

Counting the number of homomorphisms of a pattern graph H in a large input graph G is a fundamental problem in computer science. There are myriad applications of this problem in databases, graph algorithms, and network science. Often, we…

The leafage of a chordal graph G is the minimum integer l such that G can be realized as an intersection graph of subtrees of a tree with l leaves. We consider structural parameterization by the leafage of classical domination and cut…

Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred…