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Γ-Graphic Delta-Matroids and Their Applications

Authors Donggyu Kim, Duksang Lee , Sang-il Oum



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Author Details

Donggyu Kim
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea
  • Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea
Duksang Lee
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea
  • Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea
Sang-il Oum
  • Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea
  • Department of Mathematical Sciences, KAIST, Daejeon, South Korea

Cite AsGet BibTex

Donggyu Kim, Duksang Lee, and Sang-il Oum. Γ-Graphic Delta-Matroids and Their Applications. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 70:1-70:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ISAAC.2021.70

Abstract

For an abelian group Γ, a Γ-labelled graph is a graph whose vertices are labelled by elements of Γ. We prove that a certain collection of edge sets of a Γ-labelled graph forms a delta-matroid, which we call a Γ-graphic delta-matroid, and provide a polynomial-time algorithm to solve the separation problem, which allows us to apply the symmetric greedy algorithm of Bouchet to find a maximum weight feasible set in such a delta-matroid. We present two algorithmic applications on graphs; Maximum Weight Packing of Trees of Order Not Divisible by k and Maximum Weight S-Tree Packing. We also discuss various properties of Γ-graphic delta-matroids.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Matroids and greedoids
Keywords
  • delta-matroid
  • group-labelled graph
  • greedy algorithm
  • tree packing

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References

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