This website requires JavaScript.

# Aharoni's rainbow cycle conjecture holds up to an additive constant

Dec 2022

In 2017, Aharoni proposed the following generalization of theCaccetta-H\"{a}ggkvist conjecture: if \$G\$ is a simple \$n\$-vertex edge-coloredgraph with \$n\$ color classes of size at least \$r\$, then \$G\$ contains a rainbowcycle of length at most \$\lceil n/r \rceil\$. In this paper, we prove that, for fixed \$r\$, Aharoni's conjecture holds up toan additive constant. Specifically, we show that for each fixed \$r \geq 1\$,there exists a constant \$c_r\$ such that if \$G\$ is a simple \$n\$-vertexedge-colored graph with \$n\$ color classes of size at least \$r\$, then \$G\$contains a rainbow cycle of length at most \$n/r + c_r\$.

Q1论文试图解决什么问题？
Q2这是否是一个新的问题？
Q3这篇文章要验证一个什么科学假设？
0