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Are circuit diagrams two-colourable

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Filburli

Lvl 1
13y ago
Updated: 8/20/2019

A few formulations of the problem come to mind:

1:

  • Wires are edges
  • anything else is a node

In this case the characteristic graph would not always be two-colourable. As a simple counterexample take a series circuit with a battery and two loads -- this graph would not be two-colourable (one cannot two-colour a triangle).

2:

  • Junctions (anything attaching to more than two other things) are nodes
  • All others are edges

This case is a lot more interesting. If nodes can have degree greater than 3, there will be counterexamples. If nodes can only have degrees of 3, however, the graph may be two-colourable, but it must be planar (as another counterexample, consider the Petersen graph).

Well, there you have it -- please disregard the lack of formal proof

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13y ago

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