IMPROPER COLORING OF WEIGHTED GRID AND HEXAGONAL GRAPHS
2010 ◽
Vol 02
(03)
◽
pp. 395-411
◽
Keyword(s):
We study a weighted improper coloring problem motivated by a frequency allocation problem. It consists of associating to each vertex a set of p(v) (weight) distinct colors (frequencies), such that the set of vertices having a given color induces a graph of degree at most k (the case k = 0 corresponds to proper coloring). The objective is to minimize the number of colors. We propose approximation algorithms to compute such a coloring for general graphs. We apply these to obtain good approximation ratio for grid and hexagonal graphs. Furthermore we give exact results for the 2-dimensional grid and the triangular lattice when the weights are all the same.
2021 ◽
Vol 5
(1)
◽
pp. 1-31
2001 ◽
Vol 12
(04)
◽
pp. 533-550
◽
2018 ◽
Vol 7
(4.10)
◽
pp. 64
Keyword(s):
2016 ◽
Vol 33
(3)
◽
pp. 809-813
◽
2016 ◽
Vol 26
(3)
◽
pp. 281-295
◽