- Luisa Gargano ORCID:orcid.org/0000-0003-3459-107511 &
- Adele A. Rescigno ORCID:orcid.org/0000-0001-9124-610X11
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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.
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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Department of Computer Science, University of Salerno, Fisciano, Italy
Luisa Gargano & Adele A. Rescigno
- Luisa Gargano
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- Adele A. Rescigno
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Correspondence toAdele A. Rescigno.
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National Autonomous University of Mexico, Mexico, Mexico
Sergio Rajsbaum
Gran Sasso Science Institute, L’Aquila, Italy
Alkida Balliu
Arizona State University, Tempe, AZ, USA
Joshua J. Daymude
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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