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Good spanning tree

Good spanning tree is a computer science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Good spanning tree rather than just read about it. In short: In the mathematical field of graph theory, a good spanning tree T {\displaystyle T} of an embedded planar graph G {\displaystyle G} is a rooted spanning tree of G {\displaystyle G} whose non-tree edges satisfy the following conditions. there is no non-tree edge ( u , v ) {\displaystyle (u,v)} where u {\displaystyle u} and v {\displaystyle v} lie on a path from the root of T {\displaystyle T} to a leaf, the edges inc…

Good spanning tree — main illustration
Good spanning tree — illustration

Key takeaways

  • Good spanning tree belongs to computer science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Good spanning tree to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Good spanning tree from memory before moving on to harder problems.

Reference excerpt

In the mathematical field of graph theory, a good spanning tree T {\displaystyle T} of an embedded planar graph G {\displaystyle G} is a rooted spanning tree of G {\displaystyle G} whose non-tree edges satisfy the following conditions.

there is no non-tree edge ( u , v ) {\displaystyle (u,v)} where u {\displaystyle u} and v {\displaystyle v} lie on a path from the root of T {\displaystyle T} to a leaf, the edges incident to a vertex v {\displaystyle v} can be divided by three sets X v , Y v {\displaystyle X_{v},Y_{v}} and Z v {\displaystyle Z_{v}} , where,

X v {\displaystyle X_{v}} is a set of non-tree edges, they terminate in red zone

Y v {\displaystyle Y_{v}} is a set of tree edges, they are children of v {\displaystyle v}

Z v {\displaystyle Z_{v}} is a set of non-tree edges, they terminate in green zone

Formal definition Source:

… excerpt ends here. Continue reading the full article.

Illustrations

Good spanning tree: Conditions of good spanning tree
Conditions of good spanning tree
Good spanning tree: An illustration for X v , Y v {\displaystyle X_{v},Y_{v}} and Z v {\displaystyle Z_{v}} sets of edges
An illustration for X v , Y v {\displaystyle X_{v},Y_{v}} and Z v {\displaystyle Z_{v}} sets of edges
Good spanning tree: A plane graph G ϕ {\displaystyle G_{\phi }} (top), a good spanning tree T {\displaystyle T} of G ϕ {\displaystyle G_{\phi }} (down) solid edges are part of good spanning tree and dotted edges are non-tree edges in G ϕ {\displaystyle G_{\phi }} with respect to T {\displaystyle T} .
A plane graph G ϕ {\displaystyle G_{\phi }} (top), a good spanning tree T {\displaystyle T} of G ϕ {\displaystyle G_{\phi }} (down) solid edges are part of good spanning tree and dotted edges are non-tree edges in G ϕ {\displaystyle G_{\phi }} with respect to T {\displaystyle T} .

Worked examples

Example 1 — a first encounter with Good spanning tree

Start with the simplest possible case. Write down what Good spanning tree claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Good spanning tree before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Good spanning tree ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Good spanning tree

In research
Good spanning tree appears in computer science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Good spanning tree in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Good spanning tree is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational problems in graph theory, Planar graphs, Spanning tree, so understanding it makes those chapters shorter.
In everyday life
Look for Good spanning tree outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Good spanning tree in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Good spanning tree means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Good spanning tree out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Good spanning tree in simple terms?

In the mathematical field of graph theory, a good spanning tree T {\displaystyle T} of an embedded planar graph G {\displaystyle G} is a rooted spanning tree of G {\displaystyle G} whose non-tree edges satisfy the following conditions. there is no non-tree edge ( u , v ) {\displaystyle (u,v)} where…

Why does Good spanning tree matter?

Because it connects several computer science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Good spanning tree?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Good spanning tree.

Tags

  • Computational problems in graph theory
  • Planar graphs
  • Spanning tree

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