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Strong Circuit Double Cover of Some Cubic Graphs
Author(s) -
Miao Zhengke,
Tang Wenliang,
Zhang CunQuan
Publication year - 2015
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.21794
Subject(s) - conjecture , combinatorics , cubic graph , mathematics , cover (algebra) , graph , path (computing) , order (exchange) , electronic circuit , hamiltonian path , discrete mathematics , computer science , physics , line graph , quantum mechanics , voltage graph , mechanical engineering , finance , engineering , economics , programming language
Let C be a given circuit of a bridgeless cubic graph G . It was conjectured by Seymour that G has a circuit double cover (CDC) containing the given circuit C . This conjecture (strong CDC [SCDC] conjecture) has been verified by Fleischner and Häggkvist for various families of graphs and circuits. In this article, some of these earlier results have been improved: (1) if H = G − C contains a Hamilton path or a Y ‐tree of order less than 14, then G has a CDC containing C ; (2) if H = G − C is connected and | V ( H ) | ≤ 6 , then G has a CDC containing C .