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In graph theory, Mac Lane's planarity criterion is a characterisation of planar graphs in terms of their cycle spaces, named after Saunders Mac Lane who published it in 1937. It states that a finite undirected graph is planar if and only if the cycle space of the graph (taken modulo 2) has a cycle basis in which each edge of the graph ...
Mac Lane's planarity criterion, named after Saunders Mac Lane, characterizes planar graphs in terms of their cycle spaces and cycle bases. It states that a finite undirected graph is planar if and only if the graph has a cycle basis in which each edge of the graph participates in at most two basis cycles.
Mac Lane's planarity criterion gives an algebraic characterization of finite planar graphs, via their cycle spaces; The Fraysseix–Rosenstiehl planarity criterion gives a characterization based on the existence of a bipartition of the cotree edges of a depth-first search tree. It is central to the left-right planarity testing algorithm;
Mac Lane's planarity criterion uses this idea to characterize the planar graphs in terms of the cycle bases: a finite undirected graph is planar if and only if it has a sparse cycle basis or 2-basis, [3] a basis in which each edge of the graph participates in at most two basis cycles. In a planar graph, the cycle basis formed by the set of ...
Other planarity criteria, that characterize planar graphs mathematically but are less central to planarity testing algorithms, include: Whitney's planarity criterion that a graph is planar if and only if its graphic matroid is also cographic, Mac Lane's planarity criterion characterizing planar graphs by the bases of their cycle spaces,
Mac Lane coherence theorem Mac Lane set theory Mac Lane's condition Mac Lane's planarity criterion Eilenberg–MacLane space Steinitz–Mac Lane exchange lemma: Spouse: Dorothy Jones (m. 1934) Awards: Chauvenet Prize (1941) [1] [2] Leroy P. Steele Prize (1986) National Medal of Science (1989) Scientific career: Fields: Mathematical logic ...
Mac Lane's planarity criterion; Map graph; Medial graph; Meshedness coefficient; Moser spindle; N. Nested triangles graph; O. ... Whitney's planarity criterion ...
In category theory, a branch of mathematics, Mac Lane's coherence theorem states, in the words of Saunders Mac Lane, “every diagram commutes”. [1] But regarding a result about certain commutative diagrams, Kelly is states as follows: "no longer be seen as constituting the essence of a coherence theorem". [ 2 ]