Colouring a dominating set without conflicts: q-Subset Square Colouring

The Square Colouring of a graph G refers to colouring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colours. In this paper, we initiate the study of a related colouring problem called the subset square colouring of graphs. Broadly, the...

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Bibliographic Details
Published in:Theoretical computer science Vol. 976; p. 114160
Main Authors: Abidha, V.P., Ashok, Pradeesha, Tomar, Avi, Yadav, Dolly
Format: Journal Article
Language:English
Published: Elsevier B.V 17.10.2023
Subjects:
Dominating set
Graph colouring
Parameterized algorithm
Square Colouring
Subset Square Colouring
Graph colouring
Subset Square Colouring
Square Colouring
Parameterized algorithm
Dominating set
ISSN:0304-3975
Online Access:Get full text
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Summary:The Square Colouring of a graph G refers to colouring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colours. In this paper, we initiate the study of a related colouring problem called the subset square colouring of graphs. Broadly, the subset square colouring of a graph studies the square colouring of a dominating set of a graph using q colours. Here, the aim is to optimize the number of colours used. This also generalizes the well-studied Efficient Dominating Set problem. We show that the q-Subset Square Colouring problem with q=2 is NP-hard even on planar bipartite graphs and the q-Subset Square Colouring problem is NP-hard even on bipartite graphs and chordal graphs. We further study the parameterized complexity of this problem when parameterized by a number of structural parameters. We further show bounds on the number of colours needed to subset square colour some graph classes.
ISSN:0304-3975
DOI:10.1016/j.tcs.2023.114160