A 3-consecutive C-coloring of a graph G = (V,E) is a mapping ρ : V → ℕ such that every path on three vertices has at most two colors. We prove general estimates on the maximum number X3CC(G) of colors in a 3-consecutive C-coloring of G, and characterize the structure of connected graphs with X3CC(G) ≥ k for k = 3 and k = 4.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics