4 papers
On Ceva's and Menelaus's Theorems for a Möbius triangle
Ivan Livinsky
We generalize the classical Ceva's and Menelaus's theorems to curvilinear triangles bounded by circular arcs. We introduce trilinear coordinates associated with such triangles and…
EfficientDepth: A Fast and Detail-Preserving Monocular Depth Estimation Model
Andrii Litvynchuk, Ivan Livinsky, Anand Ravi +2
Monocular depth estimation (MDE) plays a pivotal role in various computer vision applications, such as robotics, augmented reality, and autonomous driving. Despite recent advanceme…
A construction for bipatite Turán numbers
Ivan Livinsky
We consider in detail the well-known family of graphs that establish an asymptotic lower bound for Turán numbers . We prove that for som…
Computation of the Ramsey Numbers and
Ivan Livinsky, Alexander Lange, Stanisław Radziszowski
The Ramsey number is the smallest such that any graph on vertices contains a cycle of length four or an independent set of order . With the help of computer…