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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16289 |
| Date | 10 July 2016 |
| Creators | Chandler, James D., Desormeaux, Wyatt J., Haynes, Teresa W., Hedetniemi, Stephen T. |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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