相关论文: Minimal Graph Embeddings via Point Deletions in St…

We introduce an impartial combinatorial game on Steiner triple systems called Nofil. Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. We explore the play of…

Let $G$ be a simple finite graph and $G'$ be a subgraph of $G$. A $G'$-design $(X,\cal B)$ of order $n$ is said to be embedded into a $G$-design $(X\cup U,\cal C)$ of order $n+u$, if there is an injective function $f:\cal B\rightarrow \cal…

We propose a new approach to studies on partial Steiner triple systems consisting in determining complete graphs contained in them. We establish the structure which complete graphs yield in a minimal PSTS that contains them. As a by-product…

Conventionally, pairwise relationships between nodes are considered to be the fundamental building blocks of complex networks. However, over the last decade the overabundance of certain sub-network patterns, so called motifs, has attracted…

The existence of Steiner triple systems STS(n) of order n containing no nontrivial subsystem is well known for every admissible n. We generalize this result in two ways. First we define the expander property of 3-uniform hypergraphs and…

Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…

Given a partial Steiner triple system (STS) of order $n$, what is the order of the smallest complete STS it can be embedded into? The study of this question goes back more than 40 years. In this paper we answer it for relatively sparse…

A Heffter array is an m by n matrix with nonzero entries from Z_{2mn+1} such that i) every row and column sum to 0, and ii) no element from {x,-x} appears twice. We construct some Heffter arrays. These arrays are used to build current…

Graph embedding is a popular algorithmic approach for creating vector representations for individual vertices in networks. Training these algorithms at scale is important for creating embeddings that can be used for classification, ranking,…

We theoretically implement a strategy from quantum computation architectures to simulate Stuart-Landau oscillator dynamics in all-to-all connected networks, also referred to as complete graphs. The technique builds upon the triad structure…

A minimal separating set in a connected topological space $X$ is a subset $L \subset X$ with the property that $X \setminus L$ is disconnected, but if $L^{\prime}$ is a proper subset of $L$, then $X \setminus L^{\prime}$ is connected. Such…

The pinched sphere is the pseudo-surface $\mathbb{S}^{\circ}_0$ obtained by identifying two distinct points of the sphere. We provide a structural characterization of graphs excluding an $\mathbb{S}^{\circ}_0$-embeddable graph as a minor.…

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…

A graph embedded in the 3-sphere is called irreducible if it is non-splittable and for any 2-sphere embedded in the 3-sphere that intersects the graph at one point the graph is contained in one of the 3-balls bounded by the 2-sphere. We…

We introduce series-triangular graph embeddings and show how to partition point sets with them. This result is then used to improve the upper bound on the number of Steiner points needed to obtain compatible triangulations of point sets.…

A graph is $n$-existentially closed ($n$-e.c.) if for any disjoint subsets $A$, $B$ of vertices with $|{A \cup B}|=n$, there is a vertex $z \notin A \cup B$ adjacent to every vertex of $A$ and no vertex of $B$. For a block design with block…

We initiate the algorithmic study of retracting a graph into a cycle in the graph, which seeks a mapping of the graph vertices to the cycle vertices, so as to minimize the maximum stretch of any edge, subject to the constraint that the…

This paper presents a framework for learning player embeddings in competitive games and events. Players and their win-loss relationships are modeled as a skill gap graph, which is an undirected weighted graph. The player embeddings are…

A graph is intrinsically projectively linked (IPL) if its every embedding in projective space contains a nonsplit link. Some minor-minimal IPL graphs have been found previously. We determine that no minor-minimal IPL graphs on 16 edges…

We study nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and the Johnson graphs. For the first eigenvalue we obtain the minimums of $L_{\infty}$-norm for several infinite series of Johnson graphs, including…