A 220-vertex <a href="https://en.wikipedia.org/wiki/Triangle-free_graph" class="extiw" title="w:Triangle-free graph">triangle-free</a> <a href="https://en.wikipedia.org/wiki/circle_graph" class="extiw" title="w:circle graph">circle graph</a> requiring five colors, the maximum of any triangle-free circle graph, as described by A. A. Ageev, <i>A triangle-free circle graph with chromatic number 5</i>, Discrete Math. <b>152</b> (1996), 295–298. The graph is represented by a chord diagram, in which each vertex is represented by a line in the <a href="https://en.wikipedia.org/wiki/hyperbolic_plane" class="extiw" title="w:hyperbolic plane">hyperbolic plane</a> and two vertices are connected by an edge whenever the corresponding two lines cross.
<a href="//commons.wikimedia.org/wiki/User:David_Eppstein" class="mw-redirect" title="User:David Eppstein">David Eppstein</a>
<span class="int-own-work" lang="en">Own work</span>