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Hamiltonian weights and unique 3‐edge‐colorings of cubic graphs
Author(s) -
Zhang CunQuan
Publication year - 1995
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.3190200110
Subject(s) - cubic graph , mathematics , combinatorics , eulerian path , hamiltonian (control theory) , hamiltonian path , graph , discrete mathematics , petersen graph , line graph , graph power , voltage graph , lagrangian , pure mathematics , mathematical optimization
A (1,2)‐eulerian weight w of a grph is hamiltonian if every faithful cover of w is a set of two Hamilton circuits. Let G be a 3‐connected cubic graph containing no subdivition of the Petersen graph. We prove that if G admits a hamiltonian weight then G is uniquely 3‐edge‐colorable. © 1996 John Wiley & Sons, Inc.
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