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We give an algorithm that, for every fixed k, decides isomorphism of graphs of rank width at most k in polynomial time. As the clique width of a graph is bounded in terms of its rank width, we also obtain a polynomial time isomorphism test…

Discrete Mathematics · Computer Science 2015-05-15 Martin Grohe , Pascal Schweitzer

In this paper we compare and illustrate the algorithmic use of graphs of bounded tree-width and graphs of bounded clique-width. For this purpose we give polynomial time algorithms for computing the four basic graph parameters independence…

Data Structures and Algorithms · Computer Science 2008-12-18 Frank Gurski

Many natural computational problems, including e.g. Max Weight Independent Set, Feedback Vertex Set, or Vertex Planarization, can be unified under an umbrella of finding the largest sparse induced subgraph, that satisfies some property…

Data Structures and Algorithms · Computer Science 2026-05-19 Maria Chudnovsky , Jadwiga Czyżewska , Kacper Kluk , Marcin Pilipczuk , Paweł Rzążewski

Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class ${\cal G}$ if they are so on the atoms (graphs with no…

Discrete Mathematics · Computer Science 2026-02-19 Konrad K. Dabrowski , Tomáš Masařík , Jana Novotná , Daniël Paulusma , Paweł Rzążewski

Clique-width is a well-known graph parameter. Many NP-hard graph problems admit polynomial-time solutions when restricted to graphs of bounded clique-width. The same holds for NLC-width. In this paper we study the behavior of clique-width…

Data Structures and Algorithms · Computer Science 2016-06-07 Frank Gurski

In the well known planted clique problem, a clique (or alternatively, an independent set) of size $k$ is planted at random in an Erdos-Renyi random $G(n, p)$ graph, and the goal is to design an algorithm that finds the maximum clique (or…

Data Structures and Algorithms · Computer Science 2020-04-29 Uriel Feige , Vadim Grinberg

We study computational complexity of the class of distance-constrained graph labeling problems from the fixed parameter tractability point of view. The parameters studied are neighborhood diversity and clique width. We rephrase the distance…

Discrete Mathematics · Computer Science 2015-12-04 Jiří Fiala , Tomáš Gavenčiak , Dušan Knop , Martin Koutecký , Jan Kratochvíl

In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…

Data Structures and Algorithms · Computer Science 2012-12-18 Mugurel Ionut Andreica

While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of…

Logic in Computer Science · Computer Science 2020-04-07 Onur Çağırıcı , Petr Hliněný , Filip Pokrývka , Abhisekh Sankaran

It is known that a number of natural graph problems which are FPT parameterized by treewidth become W-hard when parameterized by clique-width. It is therefore desirable to find a different structural graph parameter which is as general as…

Data Structures and Algorithms · Computer Science 2013-08-15 Jakub Gajarský , Michael Lampis , Sebastian Ordyniak

The $H$-Coloring problem is a well-known generalization of the classical NP-complete problem $k$-Coloring where the task is to determine whether an input graph admits a homomorphism to the template graph $H$. This problem has been the…

Computational Complexity · Computer Science 2025-09-08 Ambroise Baril , Miguel Couceiro , Victor Lagerkvist

In this paper, we study several coloring problems on graphs from the viewpoint of parameterized complexity. We show that Precoloring Extension is fixed-parameter tractable (FPT) parameterized by distance to clique and Equitable Coloring is…

Data Structures and Algorithms · Computer Science 2020-05-29 I. Vinod Reddy

The maximum stable set problem is NP-hard, even when restricted to triangle-free graphs. In particular, one cannot expect a polynomial time algorithm deciding if a bull-free graph has a stable set of size $k$, when $k$ is part of the…

Discrete Mathematics · Computer Science 2015-11-20 Stéphan Thomassé , Nicolas Trotignon , Kristina Vusković

Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems…

Data Structures and Algorithms · Computer Science 2014-05-01 Sigve Hortemo Sæther , Jan Arne Telle

An acyclic r-coloring of a directed graph G=(V,E) is a partition of the vertex set V into r acyclic sets. The dichromatic number of a directed graph G is the smallest r such that G allows an acyclic r-coloring. For symmetric digraphs the…

Data Structures and Algorithms · Computer Science 2020-11-23 Frank Gurski , Dominique Komander , Carolin Rehs

For a graph $H$, a graph $G$ is an $H$-graph if it is an intersection graph of connected subgraphs of some subdivision of $H$. $H$-graphs naturally generalize several important graph classes like interval or circular-arc graph. This class…

Data Structures and Algorithms · Computer Science 2020-02-24 Fedor V. Fomin , Petr A. Golovach , Jean-Florent Raymond

An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…

Data Structures and Algorithms · Computer Science 2022-08-29 Ahammed Ullah

We introduce a variant of the graph coloring problem, which we denote as {\sc Budgeted Coloring Problem} (\bcp). Given a graph $G$, an integer $c$ and an ordered list of integers $\{b_1, b_2, \ldots, b_c\}$, \bcp asks whether there exists a…

Data Structures and Algorithms · Computer Science 2021-10-28 Susobhan Bandopadhyay , Suman Banerjee , Aritra Banik , Venkatesh Raman

We prove that the class of $(K_t,sP_1+P_5)$-free graphs has bounded mim-width for every $s\geq 0$ and $t\geq 1$, and that there is a polynomial-time algorithm that, given a graph in the class, computes a branch decomposition of constant…

Data Structures and Algorithms · Computer Science 2020-04-27 Nick Brettell , Jake Horsfield , Daniel Paulusma

A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each pair of which is connected by an edge in E. The clique problem is an optimization problem of finding a clique of maximum size in graph. The clique problem is…

Discrete Mathematics · Computer Science 2007-10-04 Murali Krishna P , Sabu . M Thampi