Displaying similar documents to “The Mycielskian of a Graph”

Orthogonal vector coloring.

Haynes, Gerald, Park, Catherine, Schaeffer, Amanda, Webster, Jordan, Mitchell, Lon H. (2010)

The Electronic Journal of Combinatorics [electronic only]

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Relational Formal Characterization of Rough Sets

Adam Grabowski (2013)

Formalized Mathematics

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The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based...

The Friendship Theorem

Karol Pąk (2012)

Formalized Mathematics

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In this article we prove the friendship theorem according to the article [1], which states that if a group of people has the property that any pair of persons have exactly one common friend, then there is a universal friend, i.e. a person who is a friend of every other person in the group

Antichains in the homomorphism order of graphs

Dwight Duffus, Peter, L. Erdös, Jaroslav Nešetřil, Lajos Soukup (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝔾 and 𝔻 , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal...