Related papers: Games on deBruijn Graphs and Cycle Means
We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…
A generalized de Bruijn digraph generalizes a de Bruijn digraph to the case where the number of vertices need not be a pure power of an integer. Hamiltonian cycles in these digraphs thus generalize regular de~Bruijn cycles, and we will thus…
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…
We propose a formulation of a general-sum bimatrix game as a bipartite directed graph with the objective of establishing a correspondence between the set of the relevant structures of the graph (in particular elementary cycles) and the set…
In a strong game played on the edge set of a graph G there are two players, Red and Blue, alternating turns in claiming previously unclaimed edges of G (with Red playing first). The winner is the first one to claim all the edges of some…
Consider a directed or an undirected graph with integral edge weights from the set [-W, W], that does not contain negative weight cycles. In this paper, we introduce a general framework for solving problems on such graphs using matrix…
This paper analyzes the problem of assigning weights to edges incrementally in a dynamic complete bipartite graph consisting of producer and consumer nodes. The objective is to minimize the overall cost while satisfying certain constraints.…
Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…
We consider the following question. We have a dense regular graph $G$ with degree $\alpha n$, where $\alpha>0$ is a constant. We add $m=o(n^2)$ random edges. The edges of the augmented graph $G(m)$ are given independent edge weights $X(e)$,…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
Networks are often studied using the eigenvalues of their adjacency matrix, a powerful mathematical tool with a wide range of applications. Since in real systems the exact graph structure is not known, researchers resort to random graphs to…
Graph labeling is a technique that assigns unique labels or weights to the vertices or edges of a graph, often used to analyze and solve various graph-related problems. There are few methods with certain limitations conducted by researchers…
The de Bruijn torus (or grid) problem looks to find an $n$-by-$m$ binary matrix in which every possible $j$-by-$k$ submatrix appears exactly once. The existence and construction of these binary matrices was determined in the 70's, with…
Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…
We consider complete graphs with edge weights and/or node weights taking values in some set. In the first part of this paper, we show that a large number of graphs are completely determined, up to isomorphism, by the distribution of their…
Dense subgraph discovery aims to find a dense component in edge-weighted graphs. This is a fundamental graph-mining task with a variety of applications and thus has received much attention recently. Although most existing methods assume…
The Game of Cycles is a combinatorial game introduced by Francis Su in 2020 in which players take turns marking arrows on the edges of a simple plane graph, avoiding the creation of sinks and sources and seeking to complete a "cycle cell."…
Security games model strategic interactions in adversarial real-world applications. Such applications often involve extremely large but highly structured strategy sets (e.g., selecting a distribution over all patrol routes in a given…
Maximum weight matching is one of the most fundamental combinatorial optimization problems with a wide range of applications in data mining and bioinformatics. Developing distributed weighted matching algorithms is challenging due to the…