https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=79.180.69.87formulasearchengine - User contributions [en]2026-08-13T01:11:36ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Dinic%27s_algorithm&diff=24467Dinic's algorithm2014-01-20T10:34:25Z<p>79.180.69.87: /* Special cases */</p>
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<div>In [[mathematics]], a '''coreflexive relation''' is a [[binary relation]] that is a subset of the [[identity relation]].<ref>Fonseca de Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J. (2004). Transposing Relations: From Maybe Functions to Hash Tables. In Mathematics of Program Construction (p. 337).</ref> Thus if ''a'' is related to ''b'' (''aRb'') then ''a'' is equal to ''b'' (''a&nbsp;=&nbsp;b''), but if ''c'' is equal to ''d'' (''c&nbsp;=&nbsp;d'') it does not necessarily hold that ''c'' is related to&nbsp;''d''&nbsp;(''cRd'').<br />
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In [[mathematical notation]], this is: <br />
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:<math>\forall a, b \in X,\ a R b \Rightarrow \; a = b.</math><br />
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The [[identity relation]] is coreflexive by definition. Any relation that is coreflexive is thus a subset of the identity relation.<br />
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For example, consider the relation ''R'' as "equal to and odd". Over the set of positive integers, the relationship ''R'' holds over the pairs {(1,&nbsp;1),&nbsp;(3,&nbsp;3),&nbsp;...} but does not hold over {(2,&nbsp;2),&nbsp;(4,&nbsp;4),&nbsp;...}.<br />
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==Notes==<br />
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[[Category:Mathematical relations]]</div>79.180.69.87