On Graphs Derived from Posets
Meenakshi P. Wasadikar, Shriram Khanderao Nimbhorkar · Journal of the Indian Mathematical Society · 2010
A graph is associated with a poset. If the set of upper bounds of the set of lower bounds of two elements in a poset is the poset itself then we say that these two elements are adjacent in the graph. Properties of this graph are studied. It is shown that if the chromatic number of the associated graph is finite then the clique number is equal to the chromatic number. Some properties of this graph are obtained.