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Parameterized Complexity of Coupon Coloring of Graphs

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Algorithms and Discrete Applied Mathematics (CALDAM 2025)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15536))

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Abstract

Given a graph G(V, E), a q-coupon coloring of G refers to a coloring \(f : V \rightarrow [q]\) such that the following is true for all \(v \in V\): for all \(i \in [q]\), there exists \(u \in N(v)\) such that \(f(u) = i\). Given a graph G, the \(q\)-Coupon Coloring problem is to decide whether G admits a q-coupon coloring. The \(q\)-Coupon Coloring problem is shown to be NP-complete. We initiate the study of parameterized complexity of the \(q\)-Coupon Coloring problem. It is implied by existing results that parameterization by q is unlikely to admit FPT algorithms. We study the \(q\)-Coupon Coloring problem parameterized by structural parameters including neighborhood diversity, twin cover, distance to clique and treewidth of the graph. We show FPT algorithms when the parameter is neighborhood diversity, twin cover and distance to clique and prove tight lower bounds when the parameter is treewidth.

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Acknowledgement

This work has been supported by the Anusandhan National Research Foundation under grant number MTR/2023/001078.

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Authors and Affiliations

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

    Pradeesha Ashok, Pradyun Devarakonda, Shiven Phogat & Swaroop A. Ram Rayala

  2. PSG College of Technology, Coimbatore, India

    J. A. Sherin

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  1. Pradeesha Ashok
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  2. Pradyun Devarakonda
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  3. Shiven Phogat
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  4. Swaroop A. Ram Rayala
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  5. J. A. Sherin
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Correspondence to Pradeesha Ashok .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, AB, Canada

    Daya Gaur

  2. Indian Institute of Technology Hyderabad, Sangareddy, Telangana, India

    Rogers Mathew

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Ashok, P., Devarakonda, P., Phogat, S., Rayala, S.A.R., Sherin, J.A. (2025). Parameterized Complexity of Coupon Coloring of Graphs. In: Gaur, D., Mathew, R. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2025. Lecture Notes in Computer Science, vol 15536. Springer, Cham. https://doi.org/10.1007/978-3-031-83438-7_3

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  • DOI: https://doi.org/10.1007/978-3-031-83438-7_3

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