| Title: | Covering the edges of a graph with triangles |
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| Authors: | ID Bujtás, Csilla (Author)
ID Davoodi, Akbar (Author)
ID Ding, Laihao (Author)
ID Győri, Ervin (Author)
ID Tuza, Zsolt (Author)
ID Yang, Donglei (Author) |
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| Files: |  PDF - Presentation file, download (283,48 KB)
MD5: 96EE4727625D7B0BB38E7D45FC982644
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0012365X24003571
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | In a graph $G$, let $\rho_\triangle(G)$ denote the minimum size of a set of edges and triangles that cover all edges of $G$, and let $\alpha_1(G)$ be the maximum size of an edge set that contains at most one edge from each triangle. Motivated by a question of Erdős, Gallai, and Tuza, we study the relationship between $\rho_\triangle(G)$ and $\alpha_1(G)$ and establish a sharp upper bound on $\rho_\triangle(G)$. We also prove Nordhaus-Gaddum-type inequalities for the considered invariants. |
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| Keywords: | edge-disjoint triangles, edge clique covering, Nordhaus-Gaddum inequality |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 8 str. |
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| Numbering: | Vol. 348, iss. 1, article no. 114226 |
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| PID: | 20.500.12556/DiRROS-20511  |
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| UDC: | 519.17 |
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| ISSN on article: | 0012-365X |
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| DOI: | 10.1016/j.disc.2024.114226 |
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| COBISS.SI-ID: | 206292739 |
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| Note: |
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| Publication date in DiRROS: | 03.10.2024 |
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| Views: | 746 |
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| Downloads: | 424 |
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| Metadata: |    |
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