Perfect graphs are, by definition, colorable with the most limited palette possible. When coloring a graph, every node in a mutually connected cluster, or “clique,” must receive a distinct color, so ...

But in perfect graphs, you do not. As the French graph theorist Claude Berge defined them in 1961, perfect graphs require a number of colors exactly equal to the size of their largest clique.

Formulated in 1961 by mathematician Claude Berge, the conjecture states that two different types of graphs, called Berge graphs and perfect graphs, are actually the same.

Easy to say, but which graphs are perfect? This puzzle is one graph theorists have worried on for decades. They started their puzzling by looking for the “flaws” that make some graphs im perfect.

Maria Chudnovsky studies mathematical objects called graphs, which consist of dots and lines, with each line connecting two dots. "A graph is a good tool to model real-life situations where the ...

Additional studies have extended these foundations to Cartesian product graphs, demonstrating that algebraic techniques can effectively generate perfect codes in more complex graph products [3].