# Sauer, Norbert W.

## Monochromatic reachability in arc-colored digraphs ★★★

Author(s): Sands; Sauer; Woodrow

**Conjecture**For every , there exists an integer such that if is a digraph whose arcs are colored with colors, then has a set which is the union of stables sets so that every vertex has a monochromatic path to some vertex in .

Keywords:

## Monochromatic reachability or rainbow triangles ★★★

Author(s): Sands; Sauer; Woodrow

In an edge-colored digraph, we say that a subgraph is *rainbow* if all its edges have distinct colors, and *monochromatic* if all its edges have the same color.

**Problem**Let be a tournament with edges colored from a set of three colors. Is it true that must have either a rainbow directed cycle of length three or a vertex so that every other vertex can be reached from by a monochromatic (directed) path?

Keywords: digraph; edge-coloring; tournament