Covering the edges of a graph with triangles

Bujtás, Csilla (author), Davoodi, Akbar (author), Ding, Laihao (author), Győri, Ervin (author), Tuza, Zsolt (author), Yang, Donglei (author)

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.

• Language: English
• Keywords: edge-disjoint triangles, edge clique covering, Nordhaus-Gaddum inequality
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 8 str.
• Numbering: Vol. 348, iss. 1, art. 114226
• PID: 20.500.12556/RUL-161300-57bb6709-7cc1-4a07-023f-830cf48f3157
• UDC: 519.17
• ISSN on article: 0012-365X
• DOI: 10.1016/j.disc.2024.114226
• COBISS.SI-ID: 206292739
• Publication date in RUL: 09.09.2024

Record is a part of a journal

• Title: Discrete mathematics
• Shortened title: Discrete math.
• Publisher: Elsevier
• ISSN: 0012-365X
• COBISS.SI-ID: 1118479

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