Hvac Zoning And Pressurization Diagrams

HVAC Zoning and Pressurization Diagrams Four Color Map Theorem Bill Greco May , 2009 Summary HVAC Zoning and Pressurization diagrams having five or more areas require a minimum of four colors or hatch patterns, however four hatch or color patterns is also the maximum required for any plan or diagram, regardless of the number of areas or segments. Main The least number of colors or hatch patterns that is sufficient so that regions with common boudary-line segments on a plan with five or more rooms or areas are distingushed is known as the Four Color Map Theorem. The Four Color Map Theorem is a sub set of Graph Theory. Irrespective of individual size and shape , five areas cannot occupy such positions on a plan that every one of them will have a border common with all the other four.

Many eminent mathematicians worked on this conjecture including: Francis Gutherie (1831-1899) Augustus de Morgan (1806-1871) Arthur Cayley (1821-1895) P.J.Heywood (1861-1955) Gerhard Ringel (1919- ) Kenneth Appel (1932- ) Wolfgang Haken (1928- ) Phillip Franklin (1898-1965) The conjecture was finally proven in 1976 by Wolfgang Haken and Phillip Franklin of the University of Illinois, with the assistance of a computer.