Home » Author index

Sands, Bill


Graph Theory » Directed Graphs

Monochromatic reachability in arc-colored digraphs ★★★

Author(s): Sands; Sauer; Woodrow

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

Keywords:

Posted by fhavet
updated April 4th, 2017
add new comment
Graph Theory » Directed Graphs » Tournaments

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

Keywords: digraph; edge-coloring; tournament

Posted by mdevos
updated July 15th, 2008
add new comment
Syndicate content