Editing Complete bipartite graph (section)

== Examples ==
[[File:Star graphs.svg|class=skin-invert-image|thumb|upright=1.8|right|The [[Star (graph theory)|star graphs]] {{math|''K''{{sub|1,3}}}}, {{math|''K''{{sub|1,4}}}}, {{math|''K''{{sub|1,5}}}}, and {{math|''K''{{sub|1,6}}}}.]]
[[File:Zarankiewicz K4 7.svg|class=skin-invert-image|thumb|A complete bipartite graph of {{math|''K''{{sub|4,7}}}} showing that [[Turán's brick factory problem]] with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots)]]

* For any {{mvar|k}}, {{math|''K''{{sub|1,''k''}}}} is called a [[Star (graph theory)|star]].<ref name="d"/> All complete bipartite graphs which are [[Tree (graph theory)|trees]] are stars.
** The graph {{math|''K''{{sub|1,3}}}} is called a [[Claw (graph theory)|claw]], and is used to define the [[claw-free graph]]s.<ref>{{citation | last1 = Lovász | first1 = László | author1-link = László Lovász | last2 = Plummer | first2 = Michael D. | author2-link = Michael D. Plummer | isbn = 978-0-8218-4759-6 | mr = 2536865 | page = 109 | publisher = AMS Chelsea |location=Providence, RI | title = Matching theory | url = https://books.google.com/books?id=yW3WSVq8ygcC&pg=PA109 | year = 2009}}. Corrected reprint of the 1986 original.</ref>
* The graph {{math|''K''{{sub|3,3}}}} is called the [[water, gas, and electricity|utility graph]]. This usage comes from a standard mathematical puzzle in which three utilities must each be connected to three buildings; it is impossible to solve without crossings due to the [[planar graph|nonplanarity]] of {{math|''K''{{sub|3,3}}}}.<ref>{{citation|title=A Logical Approach to Discrete Math | first1=David|last1=Gries|author1-link=David Gries|first2=Fred B.|last2=Schneider|author2-link=Fred B. Schneider | publisher=Springer | year=1993|isbn=9780387941158|page=437|url=https://books.google.com/books?id=ZWTDQ6H6gsUC&pg=PA437}}.</ref>
* The maximal bicliques found as subgraphs of the digraph of a relation are called '''concepts'''. When a lattice is formed by taking meets and joins of these subgraphs, the relation has an [[heterogeneous relation#Induced concept lattice|Induced concept lattice]]. This type of analysis of relations is called [[formal concept analysis]].
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