Tootfinder

Pathfinding in Self-Deleting Graphs
Michal Dvo\v{r}\'ak, Du\v{s}an Knop, Michal Opler, Jan Pokorn\'y, Ond\v{r}ej Such\'y, Krisztina Szil\'agyi
https://arxiv.org/abs/2507.12047

Pathfinding in Self-Deleting Graphs
In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study \emph{self-deleting graphs}, introduced by Carmesin et al. (Sarah Carmesin, David Woller, David Parker, Miroslav Kulich, and Masoumeh Mansouri. The Hamiltonian cycle and travelling salesperson problems with traversal-dependent edge deletion. J. Comput. Sci.), which consist of a graph $G=(V, E)$ and a function $f\c…

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
Sergey Kurapov, Maxim Davidovsky
https://arxiv.org/abs/2506.10936 h…

Algorithmic methods of finite discrete structures. Topological graph drawing (part III)
The manuscript considers mathematical models for creating a topological drawing of a graph based on the methods of G. Ringel's vertex rotation theory. An algorithm is presented for generating a topological drawing of a flat part of a graph based on the selection of a basis for the cycle subspace C(G) using the Monte Carlo method. A steepest descent method for constructing a topological drawing of a flat subgraph is described in the manuscript. The topological drawing of a graph is constructed u…

Energy and photon centroids of spatiotemporal light pulses and consequences for their intrinsic orbital angular momentum
Titouan Gadeyne, Thierry Ruchon
https://arxiv.org/abs/2506.13535

Energy and photon centroids of spatiotemporal light pulses and consequences for their intrinsic orbital angular momentum
An ongoing debate surrounding the intrinsic transverse orbital angular momentum (OAM) attributed to spatiotemporal optical vortex (STOV) light pulses has raised the energy and photon-density centroids as two alternative frameworks to define the center of a free electromagnetic wavepacket. We herein derive, within a single formalism, lowest-order expressions for the positions and velocities of both centroids, directly applicable to an arbitrary scalar, near-paraxial and quasi-monochromatic pulse…