Abstract
The unit distance graph $\mathcal{R}$ is the graph with vertex set $\mathbb{R}^2$ in which two vertices (points in the plane) are adjacent if and only if they are at Euclidean distance 1. We prove that the circular chromatic number of $\mathcal{R}$ is at least 4, thus improving the known lower bound of $32/9$ obtained from the fractional chromatic number of $\mathcal{R}$.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.