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Spanning Trees with Few Branch Vertices in Graphs of Bounded Neighborhood Diversity

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Abstract

A branch vertex in a tree is a vertex of degree at least three. We study theNP-hard problem of constructing spanning trees with as few branch vertices as possible. This problem generalizes the famous Hamiltonian Path problem which corresponds to the case of no vertices having degree three or more. It has been extensively studied in the literature and has important applications in network design and optimization. In this paper, we study the problem of finding a spanning tree with the minimum number of branch vertices in graphs of bounded neighborhood diversity. Neighborhood diversity, a generalization of vertex cover to dense graphs, plays an important role in the design of algorithms for such graphs.

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Notes

  1. 1.

    In the following we use omit the graph nameG (e.g. we used(v), instead of\(d_G(v)\)) whenever the graph is clear from the context.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Salerno, Fisciano, Italy

    Luisa Gargano & Adele A. Rescigno

Authors
  1. Luisa Gargano

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  2. Adele A. Rescigno

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Correspondence toAdele A. Rescigno.

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Editors and Affiliations

  1. National Autonomous University of Mexico, Mexico, Mexico

    Sergio Rajsbaum

  2. Gran Sasso Science Institute, L’Aquila, Italy

    Alkida Balliu

  3. Arizona State University, Tempe, AZ, USA

    Joshua J. Daymude

  4. Gran Sasso Science Institute, L’Aquila, Italy

    Dennis Olivetti

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Gargano, L., Rescigno, A.A. (2023). Spanning Trees with Few Branch Vertices in Graphs of Bounded Neighborhood Diversity. In: Rajsbaum, S., Balliu, A., Daymude, J.J., Olivetti, D. (eds) Structural Information and Communication Complexity. SIROCCO 2023. Lecture Notes in Computer Science, vol 13892. Springer, Cham. https://doi.org/10.1007/978-3-031-32733-9_22

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