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We considerm-colorings of the edges of a complete graph, where each color class is defined semi-algebraically with bounded complexity. The casem= 2 was first studied by Alon et al., who applied this framework to obtain surprisingly strong Ramsey-type resul ...
Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
Efficient large-scale graph processing is crucial to many disciplines. Yet, while graph algorithms naturally expose massive parallelism opportunities, their performance is limited by the memory system because of irregular memory accesses. State-of-the-art ...
We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a non-constructive ...
Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...
The exploration of one-factorizations of complete graphs is the foundation of some classical sports scheduling problems. One has to traverse the landscape of such one-factorizations by moving from one of those to a so-called neighbor one-factorization. Thi ...
This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information.First, we consider two stochastic models called query-commit and price-of-information where the algori ...
In the localization game on a graph, the goal is to find a fixed but unknown target node v* with the least number of distance queries possible. In the j-th step of the game, the player queries a single node v_j and receives, as an answer to their query, th ...
