Sharif Digital Repository

In the year 1997, at 16th British Combinatorial Conference Cameron introduced a new concept called 2-simultaneous coloring. He used this concept to reformulate a conjecture of Keedwell on the existence of critical partial Latin squares of a given type. After that, other people studied special cases of this conjecture. They also studied the relation between this conjecture and other well-known conjectures in Combinatorics, such as Cycle Double Cover Conjecture (CDC). Finally, in 2004 the general case of this conjecture was proven. In first two sections, in addition to defining some fundamental concepts, we represent the relation between Latin trade and 2-simultaneous coloring. Afterwards, by...