The second author’s ω, ∆, χ conjecture proposes that every graph satisties χ ≤ d 1 2 (∆ + 1 + ω)e. In this paper we prove that the conjecture holds for all claw-free graphs. Our approach uses the structure theorem of Chudnovsky and Seymour. Along the way we discuss a stronger local conjecture, and prove that it holds for claw-free graphs with a three-colourable complement. To prove our results ...

Four new ent-kaurane diterpenoids lushanrubescensins F-I (1-4), together with 11 known ones, lasiodonin (5), oridonin (6), ponicidin (7), isodonoiol (8), isodonal (9), rabdosin B (10), rabdoternins A and B (11 and 12), enmenol (13), epinodosin (14), and inflexusin (15), were isolated from Isodon rubescens var. lushanensis, and the structures were elucidated by spectroscopic analysis. The inhibi...