Eun Jung Kim (김은정), Directed flow-augmentation
Room B332 IBS (기초과학연구원)We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that, given a directed graph G, two integers
We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that, given a directed graph G, two integers
Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk, I will present how random walks helped make progress on algorithmic problems on planar graphs. In particular, I show how random walk based (i.e., spectral) approaches led to progress …
Property testers are probabilistic algorithms aiming to solve a decision problem efficiently in the context of big-data. A property tester for a property P has to decide (with high probability correctly) whether a given input graph has property P or is far from having property P while having local access to the graph. We study …
A temporal graph is a graph whose edges are available only at specific times. In this scenario, the only valid walks are the ones traversing adjacent edges respecting their availability, i.e. sequence of adjacent edges whose appearing times are non-decreasing. Given a graph G and vertices s and t of G, Menger’s Theorem states that …
A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every
We prove that for
I will present the short proof from that for every digraph F and every assignment of pairs of integers
Katona's intersection theorem states that every intersecting family
We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular, we compare it to other systems of orientations on triples that satisfy a natural interiority condition. Such systems, P3O (partial 3-order), are a natural generalization of posets, and include the …
The Structural Theorem of the Graph Minors series of Robertson and Seymour asserts that, for every