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Mia's Math Adventure: Just in Time! is the third title of the Mia's Big Adventure Collection software series created by Kutoka Interactive. Released in 2001 in Canada and the United States , the game teaches mathematics to children between 6 and 10 years old.
The graph obtained from a squaregraph by making a vertex for each zone (an equivalence class of parallel edges of quadrilaterals) and an edge for each two zones that meet in a quadrilateral is a circle graph determined by a triangle-free chord diagram of the unit disk.
This graph is not vertex-transitive: its automorphism group has one orbit on vertices of size 8, and one of size 4.. The Chvátal graph is Hamiltonian, and plays a key role in a proof by Fleischner & Sabidussi (2002) that it is NP-complete to determine whether a triangle-free Hamiltonian graph is 3-colorable.
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Math Rabbit is a spin-off of the Reader Rabbit educational video game series. It was published by The Learning Company in 1986 for MS-DOS and Apple II . A Deluxe version was released in 1993 for MS-DOS, Mac , and Windows 3.x .
An independent set of ⌊ ⌋ vertices (where ⌊ ⌋ is the floor function) in an n-vertex triangle-free graph is easy to find: either there is a vertex with at least ⌊ ⌋ neighbors (in which case those neighbors are an independent set) or all vertices have strictly less than ⌊ ⌋ neighbors (in which case any maximal independent set must have at least ⌊ ⌋ vertices). [4]