Abstract
An anticoloring of a graph is a partial coloring of the vertices in which no two adjacent vertices are colored in distinct colors. In the basic anticoloring problem, we are given a graph G and positive integers B1,⋯, Bk, and have to determine whether there exists an anticoloring of G such that Bj vertices are colored in color j, 1 ≤ j ≤ k. This problem is known to be NP-complete, even for two colors. We deal with the anticoloring problem on the rook's graph. In general, we are able to provide sub-linear algorithms. In some particular cases, we give an explicit formula for the optimal solution.
Original language | English |
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Pages (from-to) | 1-15 |
Number of pages | 15 |
Journal | Discrete Applied Mathematics |
Volume | 188 |
Issue number | 1 |
DOIs | |
State | Published - 1 Jan 2015 |
Keywords
- Anticoloring
- Rook's graph
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics