Gryphon Patlin, Jan van den Brand: Sublinear-Time Algorithm for MST-Weight Revisited
The usual sublinear-time algorithm for minimum spanning tree builds on Kruskal's algorithm. Here, the authors build on Jarník's (also known as Prim's) algorithm. For inquiries, you may contact Pavel Veselý.

Ce Jin, Yael Kirkpatrick, Virginia Vassilevska Williams, Nicole Wein: Beyond 2-Approximation for k-Center in Graphs
The problem of k-Center is as follows: you have n points and a metric. You want to design k of the points as centers such that you minimize the largest distance from any point to its closest center. A 2-approximation algorithm is known, and this is tight as (2-epsilon)-approximation is NP-hard, when k is part of the input. The authors then give an algorithm that gives a (2-epsilon)-approximation with the caveat of an additional constant additive error. Additionally, the authors also give fine-grained lower bounds for the problem, though in the presentation, the main focus should be on the algorithm. For inquiries, you may contact Pavel Veselý.

Mahsa Derakhshan, Mohammad Roghani, Mohammad Saneian, Tao Yu: A Simple Analysis of Ranking in General Graphs
Ranking is a well-known online algorithm that outputs an approximate matching for graphs whose vertices are revealed one by one, in an online fashion. An online algorithm must match the incoming vertex to a previous vertex without any knowledge of future arrivals, and Ranking uses a random permutation, matching the incoming vertex to the first unmatched vertex in the random order. This paper gives a simplified analysis showing that it achieves an approximation ratio greater than 1/2. Familiarity with randomized algorithms is recommended, but the paper does not use advanced mathematical tools (in fact, only a couple of bounds on binomial coefficients are sufficient), so it is suitable also for bachelor students. For inquiries or more background about online matching, you may contact Pavel Veselý.

Ziad Ismaili Alaoui, Detlef Plump, Sebastian Wild: Space-Efficient Hierholzer: Eulerian Cycles in O(m) Time and O(n) Space
It is a simple exercise to find an Eulerian cycle (if it exists) in time and space linear in the number of edges. While we indeed need to spend linear time, this paper shows that we can find an Eulerian cycle in space linear in the number of *vertices*, which is much better for dense graphs. For inquiries, you may contact Pavel Veselý.