Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...

An algorithm is introduced to determine proper and stable solutions to the model matching problem. It utilizes the theory of inverses and state-space algorithms, and it guarantees a proper and stable solution to the problem when one exists. This approach is also used to determine proper and stable solutions of the two-sided matching problem. Examples are included.