The fractional chromatic number, the Hall ratio, and the lexicographic product |
| |
| Authors: | P.D. Johnson Jr. |
| |
| Affiliation: | Department of Mathematics and Statistics, Auburn University, AL 36849, USA |
| |
| Abstract: | Let χf denote the fractional chromatic number and ρ the Hall ratio, and let the lexicographic product of G and H be denoted GlexH. Main results: (i) ρ(GlexH)≤χf(G)ρ(H); (ii) if ρ(G)=χf(G) then ρ(GlexH)=ρ(G)ρ(H) for all H; (iii) χf−ρ is unbounded. In addition, the question of how big χf/ρ can be is discussed. |
| |
| Keywords: | Fractional chromatic number Hall ratio Lexicographic product |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
