A kuratowski theorem for the projective plane | Zendy

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A kuratowski theorem for the projective plane

Author(s) -

Archdeacon Dan

Publication year - 1981

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.3190050305

Subject(s) - projective plane , combinatorics , mathematics , real projective plane , plane (geometry) , graph , discrete mathematics , projective test , projective space , pure mathematics , geometry , collineation , correlation

An embedding of a graph G into a surface S is a realization of G as a subspace of S . A graph G is irreducible for S if G does not embed in S , but any proper subgraph of G does embed in S. Irreducible graphs are the smallest (with respect to containment) graphs which fail to embed on a given surface. Let I ( S ) denote the set of graphs, each with no valency 2 vertices, which are irreducible for S . Using this notation we state Kuratowski’s theorem [ 71:

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