Related papers: Arkhipov's theorem, graph minors, and linear syste…
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…
We investigate the problem $\#\mathsf{IndSub}(\Phi)$ of counting all induced subgraphs of size $k$ in a graph $G$ that satisfy a given property $\Phi$. This continues the work of Jerrum and Meeks who proved the problem to be…
The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it.…
Two-player graph games have found numerous applications, most notably in the synthesis of reactive systems from temporal specifications, but also in verification. The relevance of infinite-state systems in these areas has lead to…
Game theoretic approaches have gained traction as robust methodologies for designing distributed local algorithms that induce a desired overall system configuration in multi-agent settings. However, much of the emphasis in these approaches…
We discuss some problems related to induced subgraphs. The first problem is about getting a good upper bound for the chromatic number in terms of the clique number for graphs in which every induced cycle has length $3$ or $4$. The second…
Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…
A complete $k$-coloring of a graph $G=(V,E)$ is an assignment $\varphi:V\to\{1,\ldots,k\}$ of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one…
We study a dynamical system motivated by our earlier work on the statistical physics of social balance on graphs that can be viewed as a generalization of annihilating walks along two directions: first, the interaction topology is a…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
Oftentimes, the Shapley value becomes infeasible for games with many players. However, establishing symmetry allows for polynomial-time computation. To examine this reduction, we identify the spectrum of homogeneous group games by using an…
In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. We first introduce a new class of…
We investigate the interrelation between graph searching games and games with imperfect information. As key consequence we obtain that parity games with bounded imperfect information can be solved in PTIME on graphs of bounded DAG-width…
The UNIQUE GAMES problem is a central problem in algorithms and complexity theory. Given an instance of UNIQUE GAMES, the STRONG UNIQUE GAMES problem asks to find the largest subset of vertices, such that the UNIQUE GAMES instance induced…
Let ${\rm ex \,} {\mathcal B}$ be a minor-closed class of graphs with a set ${\mathcal B}$ of minimal excluded minors. We study (a) the asymptotic number of graphs without $k+1$ disjoint minors in ${\mathcal B}$ and (b) the properties of a…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
A perfect coloring (equivalent concepts are equitable partition and partition design) of a graph $G$ is a function $f$ from the set of vertices onto some finite set (of colors) such that every node of color $i$ has exactly $S(i,j)$…
We introduce a notion of strategies based on averaging for nonlocal games in quantum information theory. These so-called statistical strategies come in a commuting type and a more specific spatial type, which are respectively special cases…
In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking…