Graph embeddingIn topological graph theory, an embedding (also spelled imbedding) of a graph on a surface is a representation of on in which points of are associated with vertices and simple arcs (homeomorphic images of ) are associated with edges in such a way that: the endpoints of the arc associated with an edge are the points associated with the end vertices of no arcs include points associated with other vertices, two arcs never intersect at a point which is interior to either of the arcs. Here a surface is a compact, connected -manifold.
ImageAn image is a visual representation of something. An image can be a two-dimensional (2D) representation, such as a drawing, painting, or photograph, or a three-dimensional (3D) object, such as a carving or sculpture. An image may be displayed through other media, including projection on a surface, activation of electronic signals, or digital displays. Two-dimensional images can be still or animated. Still images can usually be reproduced through mechanical means, such as photography, printmaking or photocopying.
Linkless embeddingIn topological graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean space in such a way that no two cycles of the graph are linked. A flat embedding is an embedding with the property that every cycle is the boundary of a topological disk whose interior is disjoint from the graph. A linklessly embeddable graph is a graph that has a linkless or flat embedding; these graphs form a three-dimensional analogue of the planar graphs.
YouTubeYouTube, LLC is an American online video sharing and social media platform headquartered in San Bruno, California, United States. Accessible worldwide, it was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by Google and is the second most visited website, after Google Search. YouTube has more than 2.5 billion monthly users, who collectively watch more than one billion hours of videos each day. , videos were being uploaded at a rate of more than 500 hours of content per minute.
VimeoVimeo, Inc. (ˈvɪmioʊ) is an American video hosting, sharing, and services platform provider headquartered in New York City. Vimeo focuses on the delivery of high-definition video across a range of devices. Vimeo's business model is through software as a service (SaaS). They derive revenue by providing subscription plans for businesses and content creators. Vimeo provides its subscribers with tools for video creation, editing, and broadcasting, enterprise software solutions, as well as the means for video professionals to connect with clients and other professionals.
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