generated from congyu/work_with_codex
Yu Cong
89a458c76c
Introduce a "Known results" section discussing β(M1∩M2), state the Aharoni–Berger conjectures and the Davies–McDiarmid theorem, and add three bibliography entries (emlektabla16_2024, rainbow bases SIAM, berczi_partitioning_2024).
31 lines
1.9 KiB
BibTeX
31 lines
1.9 KiB
BibTeX
@misc{emlektabla16_2024,
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title = {16th Eml{\'e}kt{\'a}bla Workshop},
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year = {2024},
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howpublished = {\url{https://users.renyi.hu/~emlektab/emlektabla16.pdf}},
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note = {Workshop PDF; accessed 2026-03-26}
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}
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@article{noauthor_rainbow_nodate,
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title = {Rainbow {Bases} in {Matroids}},
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url = {https://epubs.siam.org/doi/10.1137/22M1516750},
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abstract = {Abstract. Recently, it was proved by Bérczi and Schwarcz that the problem of factorizing a matroid into rainbow bases with respect to a given partition of its ground set is algorithmically intractable. On the other hand, many special cases were left open. We first show that the problem remains hard if the matroid is graphic, answering a question of Bérczi and Schwarcz. As another special case, we consider the problem of deciding whether a given digraph can be factorized into subgraphs which are spanning trees in the underlying sense and respect upper bounds on the indegree of every vertex. We prove that this problem is also hard. This answers a question of Frank. In the second part of the article, we deal with the relaxed problem of covering the ground set of a matroid by rainbow bases. Among other results, we show that there is a linear function such that every matroid that can be factorized into bases for some can be covered by rainbow bases if every partition class contains at most 2 elements.},
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language = {en},
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urldate = {2026-03-26},
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journal = {SIAM Journal on Discrete Mathematics},
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}
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@article{berczi_partitioning_2024,
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title = {Partitioning into common independent sets via relaxing strongly base orderability},
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volume = {202},
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issn = {00973165},
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url = {https://linkinghub.elsevier.com/retrieve/pii/S0097316523000857},
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doi = {10.1016/j.jcta.2023.105817},
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language = {en},
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urldate = {2026-03-26},
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journal = {Journal of Combinatorial Theory, Series A},
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author = {Bérczi, Kristóf and Schwarcz, Tamás},
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month = feb,
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year = {2024},
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pages = {105817},
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}
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