Edge contraction
Okay kiddo, let me tell you about edge contraction.
You know how a graph is made up of vertices (points) and edges (lines connecting them)? Well, sometimes in a graph we might want to simplify it by removing certain vertices and edges. But doing that can sometimes cause problems, like leaving disconnected parts of the graph or changing the distance between certain vertices.
That's where edge contraction comes in. It's a way of removing an edge while still keeping the vertices connected.
Imagine you have a graph with four vertices: A, B, C, and D, and three edges: AB, BC, and CD. If we want to remove the edge BC, we can't just delete it or we'll end up with two disconnected parts of the graph.
Instead, we'll contract the edge by merging the two vertices connected by it (B and C) into a single new vertex, let's call it X. X will have all the edges that B and C had, but now the graph will only have three vertices: A, X, and D. The edge we removed, BC, is now gone, but the graph is still connected.
Plus, edge contraction makes other things easier too, like computing shortest paths between vertices. That's why it's such a useful tool for graph theory.
So edge contraction is like squeezing two vertices together into one, and it helps simplify graphs without making them fall apart. Pretty neat, huh?
You know how a graph is made up of vertices (points) and edges (lines connecting them)? Well, sometimes in a graph we might want to simplify it by removing certain vertices and edges. But doing that can sometimes cause problems, like leaving disconnected parts of the graph or changing the distance between certain vertices.
That's where edge contraction comes in. It's a way of removing an edge while still keeping the vertices connected.
Imagine you have a graph with four vertices: A, B, C, and D, and three edges: AB, BC, and CD. If we want to remove the edge BC, we can't just delete it or we'll end up with two disconnected parts of the graph.
Instead, we'll contract the edge by merging the two vertices connected by it (B and C) into a single new vertex, let's call it X. X will have all the edges that B and C had, but now the graph will only have three vertices: A, X, and D. The edge we removed, BC, is now gone, but the graph is still connected.
Plus, edge contraction makes other things easier too, like computing shortest paths between vertices. That's why it's such a useful tool for graph theory.
So edge contraction is like squeezing two vertices together into one, and it helps simplify graphs without making them fall apart. Pretty neat, huh?
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