eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
70:1
70:13
10.4230/LIPIcs.ISAAC.2021.70
article
Γ-Graphic Delta-Matroids and Their Applications
Kim, Donggyu
1
2
Lee, Duksang
1
2
https://orcid.org/0000-0001-9233-4195
Oum, Sang-il
2
1
https://orcid.org/0000-0002-6889-7286
Department of Mathematical Sciences, KAIST, Daejeon, South Korea
Discrete Mathematics Group, Institute for Basic Science, Daejeon, South Korea
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.70/LIPIcs.ISAAC.2021.70.pdf
delta-matroid
group-labelled graph
greedy algorithm
tree packing