Related papers: Edge and Pair Queries -- Random Graphs and Complex…
We define the Sign Game as a two-player game played on a simple undirected mathematical graph $G$. The players alternate turns, assigning vertices of $G$ either $1$ or $-1$, and edges take on the value of the product of their endvertices.…
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
We consider random-access networks with nodes representing transmitter-receiver pairs whose signals interfere with each other depending on their vicinity. Data packets arrive at the nodes over time and form queues. The nodes can be either…
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…
Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several…
We consider three variants of a partisan combinatorial game between two players, Left and Right, played on an undirected simple graph. Left is able to delete vertices (and incident edges) while Right is able to delete edges. This natural…
We study a two-player game played on undirected graphs called {\sc Trail Trap}, which is a variant of a game known as {\sc Partizan Edge Geography}. One player starts by choosing any edge and moving a token from one endpoint to the other;…
The flexibility and effectiveness of message passing based graph neural networks (GNNs) induced considerable advances in deep learning on graph-structured data. In such approaches, GNNs recursively update node representations based on their…
We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…
A large class of Positional Games are defined on the complete graph on $n$ vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given -- usually monotone -- property. Here we…
In this paper, we completely characterize the niche graphs of bipartite tournaments and find their interesting properties.
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…
We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving…
We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…
We propose the study of many new variants of two-person graph labeling games. Hardly anything has been done in this wide open field so far.
Dynamic complexity is concerned with updating the output of a problem when the input is slightly changed. We study the dynamic complexity of two-player parity games over graphs of bounded tree-width, where updates may add or delete edges,…
Testing a graph on 2-vertex- and 2-edge-connectivity are two fundamental algorithmic graph problems. For both problems, different linear-time algorithms with simple implementations are known. Here, an even simpler linear-time algorithm is…
Two problems in the search of metric characteristics on weighted undirected graphs with non-negative edge weights are being considered. The first problem: a weighted undirected graph with non-negative edge weight is given. The radius,…
Without further ado, we present the P_3-game. The P_3-game is decidable for elementary classes of graphs such as paths and cycles. From an algorithmic point of view, the connected P_3-game is fascinating. We show that the connected P_3-game…