Cayley graphs, constructed from the algebraic structure of groups, provide a natural framework for exploring complex combinatorial properties. In these graphs, vertices represent group elements ...

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.

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 ...

Among the 23 remarkable individuals who won MacArthur Foundation fellowships earlier this week, there was mathematician Maria Chudnovsky, who is married to a violist, and stringed instrument bow-maker ...

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 ...

This is a preview. Log in through your library . Abstract We obtain a sharp result that for any even 𝑛 ≥ 34, every {𝐷𝑛, 𝐷𝑛+1}-regular graph of order 𝑛 contains [𝑛/4] disjoint perfect matchings, ...

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.

Cayley Graphs And Perfect Codes Publication Trend The graph below shows the total number of publications each year in Cayley Graphs And Perfect Codes.