A note on directed 4-cycles in digraphs

2012/04/20 by Liang, Hao, Xu, Jun-Ming
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.4515

Abstract

Using some combinatorial techniques, in this note, it is proved that if α≥ 0.28866, then any digraph on n vertices with minimum outdegree at least αn contains a directed cycle of length at most 4.

Related

• When all directed cycles have length three
• Four Blocks Cycles C(k,1,1,1) in Digraphs
• Oriented cycles in digraphs of large outdegree
• Cycles of Length 4 or 8 in Graphs with Diameter 2 and Minimum Degree at Least 3
• Oriented Trees in Digraphs without Oriented 4-cycles