Strong Circuit Double Cover of Some Cubic Graphs | Zendy

Miao Zhengke | Zendy; Tang Wenliang | Zendy; Zhang CunQuan | Zendy

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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 .

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