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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: