Small Oriented Cycle Double Cover of Graphs

Small Oriented Cycle Double Cover of Graphs

A small oriented cycle double cover (SOCDC) of a bridgeless graph G on n vertices is a collection of at most n - 1 directed cycles of the symmetric orientation, G s , of G such that each arc of G s lies in exactly one of the cycles. It is conjectured that every 2-connected graph except two complete...

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Veröffentlicht in:Bulletin of the Malaysian Mathematical Sciences Society 2016, Vol.39 (1), p.219-225
Hauptverfasser: Bagheri Gh, Behrooz, Omoomi, Behnaz
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Graph theory
Graphs
Mathematics
Mathematics and Statistics
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Zusammenfassung:A small oriented cycle double cover (SOCDC) of a bridgeless graph G on n vertices is a collection of at most n - 1 directed cycles of the symmetric orientation, G s , of G such that each arc of G s lies in exactly one of the cycles. It is conjectured that every 2-connected graph except two complete graphs K 4 and K 6 has an SOCDC . In this paper, we study graphs with SOCDC and obtain some properties of the minimal counterexample to this conjecture.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-015-0169-2