Abstract
For an abelian group \(\Gamma \), a \(\Gamma \)-labelled graph is a graph whose vertices are labelled by elements of \(\Gamma \). We prove that a certain collection of edge sets of a \(\Gamma \)-labelled graph forms a delta-matroid, which we call a \(\Gamma \)-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 \(\Gamma \)-graphic delta-matroids.
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Acknowledgements
Donggyu Kim, Duksang Lee, and Sang-il Oum: Supported by the Institute for Basic Science (IBS-R029-C1). Duksang Lee: Suppored by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (NRF-2022M3J6A1063021) and the KAIST Starting Fund (KAIST-G04220016).
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Kim, D., Lee, D. & Oum, Si. \(\Gamma \)-Graphic Delta-Matroids and Their Applications. Combinatorica 43, 963–983 (2023). https://doi.org/10.1007/s00493-023-00043-6
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DOI: https://doi.org/10.1007/s00493-023-00043-6