Multigraph
View article: Nuclearity of hypergraph $C$*-algebras
Nuclearity of hypergraph $C$*-algebras Open
We partially characterize nuclearity for the recently introduced class of hypergraph C^{\ast} -algebras using a tailor-made hypergraph minor relation. The latter is generated by certain operations on hypergraphs which resemble the moves on…
View article: Expander Phase Transitions in Random Graphs: Extremal Aspects
Expander Phase Transitions in Random Graphs: Extremal Aspects Open
Expander graphs are sparse graphs with strong connectivity properties, finding wide applications in computer science, coding theory, and network design. Their presence in random graph models is a topic of significant interest, particularly…
View article: Saturation numbers of $K_{2}\vee P_{k}$
Saturation numbers of $K_{2}\vee P_{k}$ Open
A graph $G$ is called $H$-saturated if $G$ contains no copy of $H$, but $G+e$ contains a copy of $H$ for any edge $e\in E(\overline{G})$. The saturation number of $H$ is the minimum number of edges in an $H$-saturated graph of order $n$, d…
View article: Saturation numbers of $K_{2}\vee P_{k}$
Saturation numbers of $K_{2}\vee P_{k}$ Open
A graph $G$ is called $H$-saturated if $G$ contains no copy of $H$, but $G+e$ contains a copy of $H$ for any edge $e\in E(\overline{G})$. The saturation number of $H$ is the minimum number of edges in an $H$-saturated graph of order $n$, d…
View article: A Multigraph Characterization of Permutiple Strings
A Multigraph Characterization of Permutiple Strings Open
View article: Expander Phase Transitions in Random Graphs: Extremal Aspects
Expander Phase Transitions in Random Graphs: Extremal Aspects Open
Expander graphs are sparse graphs with strong connectivity properties, finding wide applications in computer science, coding theory, and network design. Their presence in random graph models is a topic of significant interest, particularly…
View article: A Multigraph Characterization of Permutiple Strings
A Multigraph Characterization of Permutiple Strings Open
View article: The Buffer Minimization Problem for Scheduling Flow Jobs with Conflicts
The Buffer Minimization Problem for Scheduling Flow Jobs with Conflicts Open
We consider the online buffer minimization in multiprocessor systems with conflicts problem (in short, the buffer minimization problem) in the recently introduced flow model. In an online fashion, workloads arrive on some of the $n$ proces…
View article: Eulerian Decomposition and the Emergence of Hamiltonicity
Eulerian Decomposition and the Emergence of Hamiltonicity Open
This paper investigates the intricate relationship between Eulerian and Hamiltonian properties in graph theory, a topic that connects two historically distinct areas of study. An Eulerian graph is characterized by the existence of a circui…
View article: Eulerian Decomposition and the Emergence of Hamiltonicity
Eulerian Decomposition and the Emergence of Hamiltonicity Open
This paper investigates the intricate relationship between Eulerian and Hamiltonian properties in graph theory, a topic that connects two historically distinct areas of study. An Eulerian graph is characterized by the existence of a circui…
View article: Efficient Algorithms and Implementations for Extracting Maximum-Size $(k,\ell)$-Sparse Subgraphs
Efficient Algorithms and Implementations for Extracting Maximum-Size $(k,\ell)$-Sparse Subgraphs Open
A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial …
View article: Efficient Algorithms and Implementations for Extracting Maximum-Size $(k,\ell)$-Sparse Subgraphs
Efficient Algorithms and Implementations for Extracting Maximum-Size $(k,\ell)$-Sparse Subgraphs Open
A multigraph $G = (V, E)$ is $(k, \ell)$-sparse if every subset $X \subseteq V$ induces at most $\max\{k|X| - \ell, 0\}$ edges. Finding a maximum-size $(k, \ell)$-sparse subgraph is a classical problem in rigidity theory and combinatorial …
View article: Eulerian Decomposition and the Emergence of Hamiltonicity
Eulerian Decomposition and the Emergence of Hamiltonicity Open
This paper investigates the intricate relationship between Eulerian and Hamiltonian properties in graph theory, a topic that connects two historically distinct areas of study. An Eulerian graph is characterized by the existence of a circui…
View article: Bounding signed bipartite partial t-trees and application to edge-coloring
Bounding signed bipartite partial t-trees and application to edge-coloring Open
Given a signed bipartite graph $(B, π)$ of negative girth $2k$, we present a necessary and sufficient condition for it to have the following property: each signed bipartite graph $(G, σ)$ whose negative girth is at least $2k$ and whose und…
View article: Bounding signed bipartite partial t-trees and application to edge-coloring
Bounding signed bipartite partial t-trees and application to edge-coloring Open
Given a signed bipartite graph $(B, π)$ of negative girth $2k$, we present a necessary and sufficient condition for it to have the following property: each signed bipartite graph $(G, σ)$ whose negative girth is at least $2k$ and whose und…
View article: The Minimum Number of Edges in $(p+1)K_2$-Saturated Graphs
The Minimum Number of Edges in $(p+1)K_2$-Saturated Graphs Open
Given a family of graphs $\mathcal{F}$, a graph $G$ is $\mathcal{F}$-saturated if it is $\mathcal{F}$-free but the addition of any missing edge creates a copy of some $F \in \mathcal{F}$. The study of the minimum number of edges in $\mathc…
View article: The Minimum Number of Edges in $(p+1)K_2$-Saturated Graphs
The Minimum Number of Edges in $(p+1)K_2$-Saturated Graphs Open
Given a family of graphs $\mathcal{F}$, a graph $G$ is $\mathcal{F}$-saturated if it is $\mathcal{F}$-free but the addition of any missing edge creates a copy of some $F \in \mathcal{F}$. The study of the minimum number of edges in $\mathc…
View article: How Many Random Edges Make an Almost-Dirac Graph Hamiltonian?
How Many Random Edges Make an Almost-Dirac Graph Hamiltonian? Open
We study Hamiltonicity in the union of an $n$-vertex graph $H$ with high minimum degree and a binomial random graph on the same vertex set. In particular, we consider the case when $H$ has minimum degree close to $n/2$. We determine the pe…
View article: The Connected Bipartite Turán Problem for Long Cycles and Paths
The Connected Bipartite Turán Problem for Long Cycles and Paths Open
Caro, Patkós, and Tuza initiated a systematic study of the bipartite Turán number for trees, and in particular asked for the extremal number of edges in connected bipartite graphs with prescribed color-class sizes that contain no paths of …
View article: The Connected Bipartite Turán Problem for Long Cycles and Paths
The Connected Bipartite Turán Problem for Long Cycles and Paths Open
Caro, Patkós, and Tuza initiated a systematic study of the bipartite Turán number for trees, and in particular asked for the extremal number of edges in connected bipartite graphs with prescribed color-class sizes that contain no paths of …
View article: Geometric Thickness of Multigraphs is $$\exists \mathbb {R}$$-Complete
Geometric Thickness of Multigraphs is $$\exists \mathbb {R}$$-Complete Open
We say that a (multi)graph $$ \user2{G} = (\user2{V},\user2{E}) $$ has geometric thickness t if there exists a straight-line drawing $$ \user2{\varphi }:\user2{V} \to \mathbb{R}^{{\mathbf{2}}} $$ and a t -coloring of its edges where no two…
View article: MemoriesDB: A Temporal-Semantic-Relational Database for Long-Term Agent Memory / Modeling Experience as a Graph of Temporal-Semantic Surfaces
MemoriesDB: A Temporal-Semantic-Relational Database for Long-Term Agent Memory / Modeling Experience as a Graph of Temporal-Semantic Surfaces Open
We introduce MemoriesDB, a unified data architecture designed to avoid decoherence across time, meaning, and relation in long-term computational memory. Each memory is a time-semantic-relational entity-a structure that simultaneously encod…
View article: Dot plot graph showing syntenic blocks between <i>C. plurivora</i> KARE80 and <i>C. paraplurivora.</i>
Dot plot graph showing syntenic blocks between <i>C. plurivora</i> KARE80 and <i>C. paraplurivora.</i> Open
Dot plot graph showing syntenic blocks between C. plurivora KARE80 and C. paraplurivora.
View article: The evolution of various notions of clustering as we vary parameters.
The evolution of various notions of clustering as we vary parameters. Open
Various clustering coefficients (columns) as we vary (x-axes) and the dimension of the node embedding (rows). From left to right, the columns show: (1) pairwise global clustering coefficient, (2) pairwise local clustering coefficient, (3) …
View article: Molecular MultiGraph and Molecular Iterative MultiGraph
Molecular MultiGraph and Molecular Iterative MultiGraph Open
A multigraph permits multiple edges between the same pair of vertices, allowing the modeling of repeated or parallel relationships in networks and systems. An iterative multigraph is obtained by repeatedly applying multigraph transformatio…
View article: Meta-Fuzzy Graph, Meta-Neutrosophic Graph, Meta-Digraph, and Meta-MultiGraph with some applications
Meta-Fuzzy Graph, Meta-Neutrosophic Graph, Meta-Digraph, and Meta-MultiGraph with some applications Open
Graph theory investigates mathematical structures consisting of vertices and edges to model relationships and connectivity [1, 2]. A MetaGraph is a higher-level graph whose vertices are themselves graphs, with edges representing specified …
View article: Network topology measures across life stages: edge density refers to the number of edges relative to the maximum number of possible edges in each graph; clustering coefficient measures the degree to which nodes in each graph cluster together; betweenness and degree centrality refer to the normalized graph level centralization measure based on the respective node-level centrality scores.
Network topology measures across life stages: edge density refers to the number of edges relative to the maximum number of possible edges in each graph; clustering coefficient measures the degree to which nodes in each graph cluster together; betweenness and degree centrality refer to the normalized graph level centralization measure based on the respective node-level centrality scores. Open
Network topology measures across life stages: edge density refers to the number of edges relative to the maximum number of possible edges in each graph; clustering coefficient measures the degree to which nodes in each graph cluster togeth…
View article: Global graphical metrics for all six learned chain graphs in this study. Edge densities represent the proportion of all possible edges that are present in the graph. The densities and number of <i>β</i> and Ω edges in each graph are shown here, along with BICs for each graph.
Global graphical metrics for all six learned chain graphs in this study. Edge densities represent the proportion of all possible edges that are present in the graph. The densities and number of <i>β</i> and Ω edges in each graph are shown here, along with BICs for each graph. Open
Global graphical metrics for all six learned chain graphs in this study. Edge densities represent the proportion of all possible edges that are present in the graph. The densities and number of β and Ω edges in each graph are shown …
View article: Edge-disjoint spanning trees and balloons in (multi-)graphs from size or spectral radius
Edge-disjoint spanning trees and balloons in (multi-)graphs from size or spectral radius Open
A multigraph is a graph that may have multiple edges, but has no loops. The multiplicity of a multigraph is the maximum number of edges between any pair of vertices. The spanning tree packing number of a graph $G$, denoted by $\tau(G)$, is…
View article: Directed graph representation with nodes (A-E) and edges indicating directional relationships between nodes.
Directed graph representation with nodes (A-E) and edges indicating directional relationships between nodes. Open
Directed graph representation with nodes (A-E) and edges indicating directional relationships between nodes.