Ore's theorem
Ore's theorem is like a special rule that helps us figure out if we can connect any two points in a graph using just one single line.
Think of a graph as a bunch of dots (that we call vertices) and lines that connect them (that we call edges). When we draw these lines, we might notice that some of the dots are really important and they connect to a lot of other dots. We call these really important dots "high-degree" vertices.
Ore's theorem says that if we have a graph with n vertices (n is just a fancy word for the number of dots we have), and we know that for any two dots, they have a total of at least n edges coming out of them combined, then we can draw a line that goes through all the dots in the graph.
This is like baking a cake, when we have all the right ingredients, like flour, sugar, eggs, and milk, we can bake a cake that is yummy and everyone will love. Similarly, when we have all these lines and dots, according to Ore's theorem we can draw a line that will help us connect all the dots.
So, in summary, Ore's theorem helps us to know if we can connect all the dots in a graph with just one single line or not. We just need to make sure that the high-degree vertices have enough edges coming out of them and then we can use Ore's Theorem to connect all the vertices.
Think of a graph as a bunch of dots (that we call vertices) and lines that connect them (that we call edges). When we draw these lines, we might notice that some of the dots are really important and they connect to a lot of other dots. We call these really important dots "high-degree" vertices.
Ore's theorem says that if we have a graph with n vertices (n is just a fancy word for the number of dots we have), and we know that for any two dots, they have a total of at least n edges coming out of them combined, then we can draw a line that goes through all the dots in the graph.
This is like baking a cake, when we have all the right ingredients, like flour, sugar, eggs, and milk, we can bake a cake that is yummy and everyone will love. Similarly, when we have all these lines and dots, according to Ore's theorem we can draw a line that will help us connect all the dots.
So, in summary, Ore's theorem helps us to know if we can connect all the dots in a graph with just one single line or not. We just need to make sure that the high-degree vertices have enough edges coming out of them and then we can use Ore's Theorem to connect all the vertices.