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Coloring a Dominating Set Without Conflicts: q-Subset Square Coloring

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Computer Science – Theory and Applications (CSR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13296))

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Abstract

The Square Coloring of a graph G refers to coloring of vertices of a graph such that any two distinct vertices which are at distance at most two receive different colors. In this paper, we initiate the study of a related coloring problem called the subset square coloring of graphs. Broadly, the subset square coloring of a graph studies the square coloring of a dominating set of a graph using q colors. Here the aim is to optimize the number of colors used. This also generalizes the well-studied Efficient Dominating Set problem. We show that the \(q\)-Subset Square Coloring problem is NP-hard for all values of q even on bipartite 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 colors needed to subset square color some graph classes.

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Notes

  1. 1.

    Proofs of results that are marked with a star are given in the full version.

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Authors and Affiliations

  1. International Institute of Information Technology Bangalore, Bangalore, India

    V. P. Abidha, Pradeesha Ashok, Avi Tomar & Dolly Yadav

Authors
  1. V. P. Abidha
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  2. Pradeesha Ashok
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  3. Avi Tomar
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  4. Dolly Yadav
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Correspondence to V. P. Abidha .

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Editors and Affiliations

  1. Steklov Institute of Mathematics, St. Petersburg, Russia

    Alexander S. Kulikov

  2. Boston University, Boston, MA, USA

    Sofya Raskhodnikova

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Abidha, V.P., Ashok, P., Tomar, A., Yadav, D. (2022). Coloring a Dominating Set Without Conflicts: q-Subset Square Coloring. In: Kulikov, A.S., Raskhodnikova, S. (eds) Computer Science – Theory and Applications. CSR 2022. Lecture Notes in Computer Science, vol 13296. Springer, Cham. https://doi.org/10.1007/978-3-031-09574-0_2

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  • DOI: https://doi.org/10.1007/978-3-031-09574-0_2

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