20.500.12556/DiRROS-20511 Covering the edges of a graph with triangles 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. edge-disjoint triangles edge clique covering Nordhaus-Gaddum inequality true false true Angleški jezik Ni določen Neznano 2024-10-03 11:29:42 2024-10-03 11:29:42 2024-10-04 03:35:24 0000-00-00 00:00:00 2025 0 0 8 str. iss. 1, article no. 114226 Vol. 348 Jan. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-01-01 519.17 0012-365X 10.1016/j.disc.2024.114226 206292739 1-s2.0-S0012365X24003571-main-1.pdf 1-s2.0-S0012365X24003571-main-1.pdf 1 96EE4727625D7B0BB38E7D45FC982644 c4c4a2007c0fb62dfbdc43bda9c5eda4a81468604f1b56bcea0b32d4aca2928f bed0cce4-816a-11ef-a5bf-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28913 https://www.sciencedirect.com/science/article/pii/S0012365X24003571 1 0611d9bb-816a-11ef-a5bf-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=28911 Inštitut za matematiko, fiziko in mehaniko 0 0 0