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On the parity of planar covers
Author(s) -
Archdeacon Dan,
Bruce Richter R.
Publication year - 1990
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.3190140208
Subject(s) - mathematics , combinatorics , planar graph , vertex (graph theory) , graph , parity (physics) , graph isomorphism , planar , isomorphism (crystallography) , discrete mathematics , line graph , computer science , crystallography , physics , chemistry , computer graphics (images) , particle physics , crystal structure
A covering is a graph map ϕ: G → H that is an isomorphism when restricted to the star of any vertex of G . If H is connected then |ϕ −1 ( v )| is constant. This constant is called the fold number . In this paper we prove that if G is a planar graph that covers a nonplanar H , then the fold number must be even.