# Finding Independent Transversals Efficiently

We give an efficient algorithm that, given a graph G and a partition V_1,...,V_m of its vertex set, finds either an independent transversal (an independent set {v_1,...,v_m} in G such that v_i∈ V_i for each i), or a subset B of vertex classes such that the subgraph of G induced by B has a small dominating set. A non-algorithmic proof of this result has been known for a number of years and has been applied to solve many other problems. Thus we are able to give algorithmic versions of many of these applications, a few of which we describe explicitly here.

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• 4 publications
research
06/28/2019

### Algorithms for weighted independent transversals and strong colouring

An independent transversal (IT) in a graph with a given vertex partition...
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03/14/2021

### Open-independent, open-locating-dominating sets: structural aspects of some classes of graphs

Let G=(V(G),E(G)) be a finite simple undirected graph with vertex set V(...
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03/11/2020

### Balanced Independent and Dominating Sets on Colored Interval Graphs

We study two new versions of independent and dominating set problems on ...
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07/28/2022

### ZDD-Based Algorithmic Framework for Solving Shortest Reconfiguration Problems

Given a graph G and two independent sets S, T of G, the independent set ...
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02/12/2020

### Algorithmic Complexity of Isolate Secure Domination in Graphs

A dominating set S is an Isolate Dominating Set (IDS) if the induced sub...
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07/28/2020

### Twin-width III: Max Independent Set and Coloring

We recently introduced the graph invariant twin-width, and showed that f...
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07/17/2021

### On the Kernel and Related Problems in Interval Digraphs

Given a digraph G, a set X⊆ V(G) is said to be absorbing set (resp. domi...