Halin's Grid Theorem is a result in graph theory that describes the structure of certain infinite graphs. Specifically, it focuses on a type of infinite graph known as a "grid" graph, which is a graph that resembles a two-dimensional grid or lattice. Halin's theorem provides conditions under which such infinite grid graphs can be embedded into three-dimensional space without crossings.
The Kelmans–Seymour conjecture is a conjecture in graph theory that relates to the structure of certain types of graphs. Specifically, it deals with the behavior of complete graphs and the existence of specific subgraphs within them. Formulated by Paul Kelmans and Neil Seymour, the conjecture states that every 2-edge-connected graph can be represented as a graph obtained from a complete graph by the contraction of edges.
Partial k-tree by Wikipedia Bot 0
A Partial k-tree is a data structure used primarily in the field of combinatorial optimization and computer science, particularly in topics related to the representation of combinatorial objects or configurations, such as combinations, subsets, or sequences. In general, a k-tree is a tree structure that represents all possible configurations of k elements chosen from a larger set, and it can be used for various applications, including generating combinations or permutations.
Petersen family by Wikipedia Bot 0
The term "Petersen family" can refer to different contexts depending on the specific area of interest. Here are a few possibilities: 1. **Cultural or Historical Context**: The Petersen family could refer to a family of historical or cultural significance in a specific region or country. 2. **Literary or Film Reference**: There might be fictional works, books, or movies that feature a "Petersen family" as characters.
In graph theory, a **Blossom** refers to a specific structure that is relevant in the context of matching algorithms, particularly in the matching of general graphs. The Blossom structure is utilized to handle situations where augmenting paths may be of odd length, which can complicate the process of finding maximum matchings. The concept of Blossoms is associated with the **Edmonds' Blossom Algorithm**, developed by Jack Edmonds in the 1960s.
Bipartite half by Wikipedia Bot 0
"Bipartite half" might refer to concepts within graph theory, particularly regarding bipartite graphs. A **bipartite graph** is a type of graph where the set of vertices can be divided into two distinct sets such that no two graph vertices within the same set are adjacent.
Clique graph by Wikipedia Bot 0
A **clique graph** is a concept in graph theory that pertains to representing cliques within a given graph. A **clique** in a graph is a subset of its vertices such that every two distinct vertices in the subset are adjacent, meaning there is an edge connecting each pair of vertices. In simpler terms, a clique is a complete subgraph.
An acyclic orientation of a directed graph (digraph) is an assignment of directions to the edges of the graph such that there are no directed cycles.
Time-sharing systems represent a significant evolution in computing, allowing multiple users to interact with a computer simultaneously. This concept emerged from the need for more efficient use of computing resources, which were, at the time, expensive and limited. ### Key Stages in the Evolution of Time-Sharing Systems: 1. **Early Computing (1950s)**: - Computers were large, expensive, and primarily used for batch processing.
Complement graph by Wikipedia Bot 0
In graph theory, the complement of a graph is a graph that contains the same set of vertices but has edges that are not present in the original graph.
The disjoint union of graphs is a concept in graph theory that combines two or more graphs into a new graph in such a way that the original graphs do not share any vertices or edges. Here's how it works: 1. **Graphs Involved**: Suppose you have two or more graphs \( G_1, G_2, \ldots, G_n \).
The Goldberg–Coxeter construction is a method used in geometry, particularly in the study of polyhedra and polyhedral structures. It provides a systematic way to generate a class of convex polyhedra, particularly those that can be described as geometric realizations of certain types of combinatorial structures known as "spherical polyhedra.
Line graph by Wikipedia Bot 0
A line graph is a type of chart used to display information that changes over time. It consists of a series of data points, called "markers," connected by straight line segments. Line graphs are particularly useful for showing trends, patterns, and relationships between two variables. ### Key Features of Line Graphs: 1. **Axes**: - The horizontal axis (x-axis) typically represents the independent variable (often time).
Moral graph by Wikipedia Bot 0
A **moral graph** is a concept used in the fields of graph theory and probabilistic graphical models, particularly in the context of Bayesian networks and Markov networks. The moral graph is derived from a directed acyclic graph (DAG) representing a Bayesian network. ### How to Construct a Moral Graph: 1. **Start with a Directed Graph:** Begin with a Bayesian network, which is typically represented as a directed acyclic graph (DAG).
Mycielskian by Wikipedia Bot 0
In mathematics and graph theory, a Mycielski graph, or Mycielski construction, is a method for constructing new graphs from existing ones. The Mycielski construction is used primarily to create triangle-free graphs, which are graphs that do not contain any cycles of length three (triangles). The construction works as follows: 1. **Start with a graph \( G \)**: This can be any simple graph.
Type-in program by Wikipedia Bot 0
A Type-in program refers to a type of computer program where the user is expected to manually enter (or "type in") the code into a computer or programming environment. This practice was particularly popular in the early days of personal computing, especially in the 1980s and 1990s, when magazines and books would publish source code listings for users to type into their own computers. Type-in programs often serve as a way to teach programming concepts, allowing users to learn by doing.
Univac Text Editor is a software tool developed for text editing on Univac computers, which were among the earliest computer systems used for business and scientific applications. Univac, short for Universal Automatic Computer, was one of the first successful commercial computer brands, developed in the 1950s and 1960s. The Univac Text Editor specifically allowed users to create, modify, and manage text documents on these systems.
Internet Plus by Wikipedia Bot 0
"Internet Plus" is a concept that originates from China, introduced by the Chinese government in 2015. It refers to the integration of the Internet with various sectors of the economy and society to foster innovation and enhance efficiency. The idea behind Internet Plus is to leverage the capabilities of the Internet — such as data connectivity, big data, cloud computing, and mobile technologies — to improve traditional industries and stimulate new modes of production and consumption.
Chordal completion, also known as chordal graph completion, refers to the process of transforming a given graph into a chordal graph. A chordal graph (or "perfect graph") is defined as a graph in which every cycle of four or more vertices has a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle. The process of chordal completion involves adding edges to the original graph in such a way that the resulting graph becomes chordal.
In graph theory, a **clique** is a subset of vertices in an undirected graph such that every two distinct vertices in the clique are adjacent. In simpler terms, a clique is a complete subgraph where every vertex is connected to every other vertex. More formally, a clique of size \( k \) is a set of \( k \) vertices such that there are edges between every pair of vertices in that set.

Pinned article: ourbigbook/introduction-to-the-ourbigbook-project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact