Math 2.0

Combinatorics Definition

Bridge

Builds on Connected component

Definition

Let GG be a graph and let ee be an edge of GG. Let G−eG - e be the graph that GG gives when ee is deleted and all vertices are kept. The edge ee is a bridge of GG if G−eG - e has more connected components than GG.

Remarks

Let e=uve = uv. Then ee is a bridge if and only if uu and vv are not reachable from each other in G−eG - e. In this case, deleting ee increases the number of components by exactly one. In a tree every edge is a bridge. In a cycle graph no edge is a bridge. Bridges are the edges on no cycle.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

Show the path as a graph
Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionReachability, definition, no evidence levelReachabilitydefinitionConnected component, definition, no evidence levelConnected componentdefinitionBridge, definition, no evidence levelBridgedefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Reachability definition
  4. Connected component definition
  5. Bridge definition

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Bridge_(graph_theory), lead section
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