Neighborhood-Restricted [≤2]-Achromatic Colorings
A (closed) neighborhood-restricted [≤2]-coloring of a graph G is an assignment of colors to the vertices of G such that no more than two colors are assigned in any closed neighborhood, that is, for every vertex v in G, the vertex v and its neighbors are in at most two different color classes. The [≤2]-achromatic number is defined as the maximum number of colors in any [≤2]-coloring of G. We study the [≤2]-achromatic number. In particular, we improve a known upper bound and characterize the extremal graphs for some other known bounds.
Chandler, James D.; Desormeaux, Wyatt J.; Haynes, Teresa W.; and Hedetniemi, Stephen T.. 2016. Neighborhood-Restricted [≤2]-Achromatic Colorings. Discrete Applied Mathematics. Vol.207 39-44. https://doi.org/10.1016/j.dam.2016.02.023 ISSN: 0166-218X