science

Multipartite graph

Multipartite graph is a 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 Multipartite graph rather than just read about it. In short: In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color.

Key takeaways

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

Reference excerpt

In graph theory, a part of mathematics, a k-partite graph is a graph whose vertices are (or can be) partitioned into k different independent sets. Equivalently, it is a graph that can be colored with k colors, so that no two endpoints of an edge have the same color. When k = 2 these are the bipartite graphs, and when k = 3 they are called the tripartite graphs. Bipartite graphs may be recognized in polynomial time but, for any k > 2 it is NP-complete, given an uncolored graph, to test whether it is k-partite. However, in some applications of graph theory, a k-partite graph may be given as input to a computation with its coloring already determined; this can happen when the sets of vertices in the graph represent different types of objects. For instance, collaborative tagging has been modelled mathematically by tripartite graphs in which the three sets of vertices in the graph represent users of a system, resources that the users are tagging, and tags that the users have applied to the resources.

A complete k-partite graph is a k-partite graph in which there is an edge between every pair of vertices from different independent sets. These graphs are described by notation with a capital letter K subscripted by a sequence of the sizes of each set in the partition. For instance, K2,2,2 is the complete tripartite graph of a regular octahedron, which can be partitioned into three independent sets each consisting of two opposite vertices. A complete multipartite graph is a graph that is complete k-partite for some k. The Turán graphs are the special case of complete multipartite graphs in which the independent sets differ in size by at most one vertex. Complete k-partite graphs, complete multipartite graphs, and their complement graphs, the cluster graphs, are special cases of cographs, and can be recognized in polynomial time even when the partition is not supplied as part of the input.

References

Illustrations

Worked examples

Example 1 — a first encounter with Multipartite graph

Start with the simplest possible case. Write down what Multipartite graph claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In 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 Multipartite graph 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 Multipartite graph 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 Multipartite graph

In research: Multipartite graph appears in 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 Multipartite graph 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: Multipartite graph is common in secondary-school and first-year university syllabi. It links to neighbouring topics Graph families, NP-complete problems, so understanding it makes those chapters shorter.
In everyday life: Look for Multipartite graph 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.

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Multipartite graph in 20 minutes

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

Frequently asked questions

What is Multipartite graph in simple terms?

Why does Multipartite graph matter?

Because it connects several 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 Multipartite graph?

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 Multipartite graph.