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- W2317509399 abstract "Let the genus of an orientable 2-manifold M be denoted by γ(M). The genus, γ( G ), of a graph G is then the smallest of the numbers γ( N ) for orientable 2-manifolds N in which G can be embedded. An embedding of G in M is called minimal if γ( G ) = γ(M). When each component of the complement of G in M is an open 2-cell, the embedding of G in M is called a 2-cell embedding. In (3), J. W. T. Youngs has shown that each minimal embedding is a 2-cell embedding. It follows from the results of (3) that for each graph G , there is a number d(G), called the regional number, such that for any 2-cell embedding of G in an orientable 2-manifold, the number of (2-cell) complementary domains of G is ⩽ d(G) , with equality holding if and only if the embedding is minimal." @default.
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- W2317509399 date "1966-01-01" @default.
- W2317509399 modified "2023-09-27" @default.
- W2317509399 title "The Genus, Regional Number, and Betti Number of a Graph" @default.
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- W2317509399 doi "https://doi.org/10.4153/cjm-1966-081-6" @default.
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