Some progress on $t$-tone coloring
By: Patrick Bennett, Jade Nichols
Potential Business Impact:
Colors graph parts so nearby ones share fewer colors.
A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For example we prove a new result for trees of large maximum degree, as well as some results for the cartesian power of a graph. We also make a conjecture about trees.
Similar Papers
Independent sets and colorings of $K_{t,t,t}$-free graphs
Combinatorics
Helps computers color maps with fewer colors.
Independent sets and colorings of $K_{t,t,t}$-free graphs
Combinatorics
Finds big groups of friends in tricky social networks.
Coloring Graphs with no Totally Odd Clique Immersion
Combinatorics
Colors graphs with no special pattern.