The Fa,b,c conjecture, I

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and one part of the conjecture was proved. The conjecture completely determines all finite members of the family. Here we prove another part of the conjecture and foreshadow a paper which completes the proof of the other three parts.

The Fa,b,c conjecture is true, II

In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. (c) 2006 Elsevier Inc. All rights reserved.

SCOTROC 2A: Carboplatin followed by docetaxel or docetaxel gemcitabine as first-line chemotherapy for ovarian cancer

The feasibility of sequential carboplatin followed by docetaxel-based therapy for untreated ovarian cancer was determined. Patients received four q3w cycles of carboplatin AUC 7, then four q3w cycles of either docetaxel 100 mg m(-2) (day 1) (arm A); docetaxel 75 mg m(-2) (day 8) and gemcitabine 1250 mg m(-2) (days 1,8) (arm B) or docetaxel 25 mg m(-2) and gemcitabine 800 mg m(-2) (both given weekly (days 1,8,15)) (arm C). A total of 44 patients were randomised to each treatment arm. None of the arms demonstrated an eight cycle completion rate (70.5/72.7/45.5% in arms A/B/C, respectively), which was statistically greater than 60% (P = 0.102, P = 0.056, P = 0.982) which was our formal feasibility criteria, although only the completion rate in arm C was clearly worse than this level. The overall response rate (ORR) after carboplatin was 65.7% in 70 evaluable patients. In evaluable patients, ORRs after docetaxel-based cycles were: arm A 84.0% (21 out of 25); arm B 77.3% (17 out of 22); arm C 69.6% (16 out of 23). At follow-up (median 30 months), median progression-free survival times were: arm A 15.5 months (95% Cl: 10.5 - 20.6); arm B 18.1 months (95% Cl: 15.9 - 20.3); arm C, 13.7 months (95% Cl: 12.8 - 14.6). Neutropenia was the predominant grade 3 - 4 haematological toxicity: 77.8/85.7/54.4% in arms A/B/C, respectively. Dyspnoea was markedly increased in both gemcitabine-containing arms (P = 0.001) but was worse in arm C. Although just failing to rule out eight cycle completion rates less than 60%, within the statistical limitations of these small cohorts, the overall results for arms A and B are encouraging. Larger phase III studies are required to test these combinations.