Small oriented cycle double cover of graphs
Behrooz Bagheri Gh., Behnaz Omoomi

TL;DR
This paper investigates the existence of small oriented cycle double covers in bridgeless graphs, explores properties of potential minimal counterexamples, and advances understanding of a conjecture related to 2-connected graphs.
Contribution
It studies graphs with small oriented cycle double covers and characterizes properties of minimal counterexamples to the conjecture.
Findings
Identifies properties of minimal counterexamples
Provides partial results supporting the conjecture
Analyzes structural aspects of graphs with SOCDC
Abstract
A small oriented cycle double cover (SOCDC)} of a bridgeless graph on vertices is a collection of at most directed cycles of the symmetric orientation, , of such that each edge of lies in exactly one of the cycles. It is conjectured that every 2-connected graph except two complete graphs and has an . In this paper, we study graphs with and obtain some properties of the minimal counterexample to this conjecture.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems
