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On the number of colorings of a snark minus an edge
Author(s) -
Bradley Richard C.
Publication year - 2006
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.20133
Subject(s) - mathematics , combinatorics , enhanced data rates for gsm evolution , discrete mathematics , computer science , artificial intelligence
For a given snark G and a given edge e of G , let ψ( G , e ) denote the nonnegative integer such that for a cubic graph conformal to G – { e }, the number of Tait colorings with three given colors is 18 · ψ( G , e ). If two snarks G 1 and G 2 are combined in certain well‐known simple ways to form a snark G , there are some connections between ψ ( G 1 , e 1 ), ψ ( G 2 , e 2 ), and ψ( G , e ) for appropriate edges e 1 , e 2 , and e of G 1 , G 2 , and G . As a consequence, if j and k are each a nonnegative integer, then there exists a snark G with an edge e such that ψ( G , e ) = 2 j · 3 k . © 2005 Wiley Periodicals, Inc.