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{"slip": { "id": 200, "advice": "Sarcasm is the lowest form of wit. Employ correctly with apt timing."}}
{"slip": { "id": 119, "advice": "Don't assume anything is possible or impossible until you've asked the people who will be doing the work."}}
{"fact":"Cats can be taught to walk on a leash, but a lot of time and patience is required to teach them. The younger the cat is, the easier it will be for them to learn.","length":161}
{"slip": { "id": 46, "advice": "Try going commando to an important meeting, NB: don't wear a skirt."}}
{"fact":"In Holland\u2019s embassy in Moscow, Russia, the staff noticed that the two Siamese cats kept meowing and clawing at the walls of the building. Their owners finally investigated, thinking they would find mice. Instead, they discovered microphones hidden by Russian spies. The cats heard the microphones when they turned on.","length":318}
{"type":"standard","title":"Gallai–Hasse–Roy–Vitaver theorem","displaytitle":"Gallai–Hasse–Roy–Vitaver theorem","namespace":{"id":0,"text":""},"wikibase_item":"Q5518852","titles":{"canonical":"Gallai–Hasse–Roy–Vitaver_theorem","normalized":"Gallai–Hasse–Roy–Vitaver theorem","display":"Gallai–Hasse–Roy–Vitaver theorem"},"pageid":36620043,"thumbnail":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Gallai-Hasse-Roy-Vitaver_theorem.svg/330px-Gallai-Hasse-Roy-Vitaver_theorem.svg.png","width":320,"height":186},"originalimage":{"source":"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Gallai-Hasse-Roy-Vitaver_theorem.svg/621px-Gallai-Hasse-Roy-Vitaver_theorem.svg.png","width":621,"height":360},"lang":"en","dir":"ltr","revision":"1274060564","tid":"f5ca8adf-e398-11ef-a102-4dd747db9a1d","timestamp":"2025-02-05T08:12:37Z","description":"Duality of graph colorings and orientations","description_source":"local","content_urls":{"desktop":{"page":"https://en.wikipedia.org/wiki/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem","revisions":"https://en.wikipedia.org/wiki/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem?action=history","edit":"https://en.wikipedia.org/wiki/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem?action=edit","talk":"https://en.wikipedia.org/wiki/Talk:Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem"},"mobile":{"page":"https://en.m.wikipedia.org/wiki/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem","revisions":"https://en.m.wikipedia.org/wiki/Special:History/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem","edit":"https://en.m.wikipedia.org/wiki/Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem?action=edit","talk":"https://en.m.wikipedia.org/wiki/Talk:Gallai%E2%80%93Hasse%E2%80%93Roy%E2%80%93Vitaver_theorem"}},"extract":"In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that the minimum number of colors needed to properly color any graph equals one plus the length of a longest path in an orientation of chosen to minimize this path's length. The orientations for which the longest path has minimum length always include at least one acyclic orientation.","extract_html":"
In graph theory, the Gallai–Hasse–Roy–Vitaver theorem is a form of duality between the colorings of the vertices of a given undirected graph and the orientations of its edges. It states that the minimum number of colors needed to properly color any graph ![](\"https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b\")
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