Rainbow C_4's and Directed C_4's: the Bipartite Case Study
Bo Ning, Jun Ge
TL;DR
This paper establishes new conditions for the existence of directed and rainbow cycles of length 4 in bipartite graphs, confirming a conjecture and providing insights into cycle existence in bipartite structures.
Contribution
It introduces a new sufficient condition for directed 4-cycles in bipartite graphs and confirms a related conjecture, also applying these results to rainbow cycles in edge-colored bipartite graphs.
Findings
New sufficient condition for directed 4-cycles in bipartite graphs
Confirmation of H. Li's conjecture on cycle existence
Application to rainbow cycles in bipartite edge-colored graphs
Abstract
In this paper we obtain a new sufficient condition for the existence of directed cycles of length 4 in oriented bipartite graphs. As a corollary, a conjecture of H. Li is confirmed. As an application, a sufficient condition for the existence of rainbow cycles of length 4 in bipartite edge-colored graphs is obtained.
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