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Polynomial Kernels for Spanning Tree with Diversity Requirements

Authors Petr A. Golovach , Diptapriyo Majumdar , Saket Saurabh

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Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Parameterized Complexity
  • Kernelization
  • Diverse Solutions
  • Diverse Spanning Trees

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Abstract

Given a connected undirected graph G, a spanning tree is a subgraph T of G such that V(T) = V(G) and T is a tree. A collection of 𝓁 spanning trees T₁,…,T_{𝓁} is {{pairwise k-diverse}} if for every i ≠ j, |E(T_i) △ E(T_j)| ≥ k. Given a connected undirected graph G and integers p, q, k, 𝓁, {Leaf&Internal-Constrained Diverse Spanning Trees} asks whether there are 𝓁 distinct spanning trees T₁,…,T_{𝓁} of G that are {{pairwise k-diverse}} such that each tree has at least p leaves and at least q internal vertices. Similarly, {Leaf&Non-terminal-Constrained Diverse Spanning Trees} takes a connected undirected graph G, V_NT ⊆ V(G), and three integers p, k, 𝓁, and asks if G has 𝓁 spanning trees that are {{pairwise k-diverse}}, and each has at least p leaves and contains the vertices of V_NT as internal. We consider these two problems from the kernelization perspective and provide polynomial kernels for {Leaf&Internal-Constrained Diverse Spanning Trees} and {Leaf&Non-terminal-Constrained Diverse Spanning Trees}, when parameterized by p + q + k + 𝓁 and p + |V_NT| + k + 𝓁, respectively.

Cite As Get BibTex

Petr A. Golovach, Diptapriyo Majumdar, and Saket Saurabh. Polynomial Kernels for Spanning Tree with Diversity Requirements. In 52nd International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 376, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.WG.2026.18

Author Details

Petr A. Golovach
  • University of Bergen, Norway
Diptapriyo Majumdar
  • Indraprastha Institute of Information Technology Delhi, New Delhi, India
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

  • Golovach, Petr A.: Supported by the Research Council of Norway via BWCA (grant 314528) and Extreme-Algorithms (grant 355137) projects.
  • Majumdar, Diptapriyo: Partially supported by Science and Engineering Research Board (SERB) grant SRG/2023/001592
  • Saurabh, Saket: Supported by European Research Council under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 819416)

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