Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4649748 | Discrete Mathematics | 2009 | 10 Pages |
Abstract
For a graph GG on nn vertices with chromatic number χ(G)χ(G), the Nordhaus–Gaddum inequalities state that ⌈2n⌉≤χ(G)+χ(G¯)≤n+1, and n≤χ(G)⋅χ(G¯)≤⌊(n+12)2⌋. Much analysis has been done to derive similar inequalities for other graph parameters, all of which are integer-valued. We determine here the optimal Nordhaus–Gaddum inequalities for the circular chromatic number and the fractional chromatic number, the first examples of Nordhaus–Gaddum inequalities where the graph parameters are rational-valued.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
J.I. Brown, R. Hoshino,