Balanced Black and White Coloring Problem on knights chessboards
نویسندگان
چکیده
Graph anticoloring problem is partial coloring problem where the main feature is the opposite rule of the graph coloring problem, i.e., if two vertices are adjacent, their assigned colors must be the same or at least one of them is uncolored. In the same way, Berge in 1972 proposed the problem of placing b black queens and w white queens on a n× n chessboard such that no two queens of different color can attack to each other, the complexity of this problem remains open. In this work we deal with the knight piece under the balance property, since this special case is the most difficult for brute force algorithms.
منابع مشابه
The Black-and-White Coloring Problem on Trees
Given a graph G and positive integers b and w, the black-and-white coloring problem asks about the existence of a partial vertex-coloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. We suggest an improved algorithm for solving this problem on trees. Submitted: June 2008 Reviewed: February 2009 Revised: March 2009 Accepted: Marc...
متن کاملThe Black-and-White Coloring Problem on Chordal Graphs
Given a graph G and positive integers b and w, the black-and-white coloring problem asks about the existence of a partial vertex-coloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. This problem is known to be NPcomplete in general. We provide here a polynomial time algorithm for chordal graphs. Submitted: September 2009 Review...
متن کاملThe black-and-white coloring problem on permutation graphs
Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B| = b and |W| = w such that no vertex in B is adjacent to any vertex in W. In this paper we show that the problem is polynomial when restricted to permutation graphs.
متن کاملThe Black-and-White Coloring Problem on Distance-Hereditary Graphs and Strongly Chordal Graphs
Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B| = b and |W| = w such that no vertex in B is adjacent to any vertex inW. In this paper we show that the problem is polynomial when restricted to cographs, distance-hereditary graphs, interval graphs and strongly chordal graphs. We show that the problem is NP-c...
متن کاملAntioxidant Effect of Orange Peel Extract on Chemical Quality, Sensory Properties, and Black Spots of Farmed White Shrimp
Background: Black spots are a major problem in commercial shrimp species and can have negative effects on shrimps' appearance, quality, shelf life, economic value, and product acceptance by consumers. This study was conducted to investigate the effect of orange peel extract on chemical and sensory qualities as well as black spots on Litopenaeus vannamei species of white farmed shrimp. Methods: ...
متن کامل