The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf
.
New results in t-tone coloring of graphs
[article]
2011
arXiv
pre-print
A t-tone k-coloring of G assigns to each vertex of G a set of t colors from {1,..., k} so that vertices at distance d share fewer than d common colors. The t-tone chromatic number of G, denoted τ_t(G), is the minimum k such that G has a t-tone k-coloring. Bickle and Phillips showed that always τ_2(G) < [Δ(G)]^2 + Δ(G), but conjectured that in fact τ_2(G) < 2Δ(G) + 2; we confirm this conjecture when Δ(G) < 3 and also show that always τ_2(G) <(2 + √(2))Δ(G). For general t we prove that τ_t(G) <
arXiv:1108.4751v1
fatcat:r4qamkdqzvhpfaijp2zahne2x4