Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

Towards a Normative Defence of Provocation in England and Ireland

This article compares, in the light of the House of Lords’ decision in R v Smith (Morgan James), the English and Irish approaches to the objective test in provocation. Though the law on this point has developed in radically different directions as between England and Ireland, both jurisdictions demonstrate a profound dissatisfaction with the objective test in its traditional formulation combined with a reluctance to dispense with it altogether. It is suggested that Lord Hoffmann’s approach in Morgan Smith, by drawing out the essentially normative function of the objective test, provides a useful way forward for the law on both sides of the Irish Sea.

The Effects of Social Class and Ethnicity on Gender Differences in GCSE Attainment: A Secondary Analysis of the Youth Cohort Study of England and Wales 1997-2001

This article is based upon a secondary analysis of the Youth Cohort Study of England and Wales 1998 and examines the effects of social class and ethnicity on gender differences in GCSE attainment for those who left school in 1997 (n = 14,662). The article shows that both social class and ethnicity exert a far greater influence on the GCSE performance of boys and girls than gender. Moreover, the article also shows that an interaction effect is present between social class and gender and also between ethnicity and gender in relation to their impact upon GCSE attainment. More specifically, the findings suggest that a strong correlation exists such that the lower the overall levels of educational attainment for any group (whether that group is defined in terms of social class or ethnicity), the higher the gender differences that exist between those within that group.