Restricted triangulation on circulant graphs

The restricted triangulation existence problem on a given graph decides whether there exists a triangulation on the graph’s vertex set that is restricted with respect to its edge set. Let G = C ( n , S ) be a circulant graph on n vertices with jump value set S . We consider the restricted triangulation existence problem for G . We determine necessary and sufficient conditions on S for which G admitting a restricted triangulation. We characterize a set of jump values S ( n ) that has the smallest cardinality with C ( n , S ( n )) admits a restricted triangulation. We present the measure of non-triangulability of K n − G for a given G

Packing 1-plane Hamiltonian cycles in complete geometric graphs

Counting the number of Hamiltonian cycles that are contained in a geometric graph is #P-complete even if the graph is known to be planar [15]. A relaxation for problems in plane geometric graphs is to allow the geometric graphs to be 1-plane, that is, each of its edges is crossed at most once. We consider the following question: For any set P of n points in the plane, how many 1-plane Hamiltonian cycles can be packed into a complete geometric graph Kn? We investigate the problem by taking two different situations of P, namely, when P is in convex position, wheel configurations position. For points in general position we prove the lower bound of k − 1 where n = 2k + h and 0 ≤ h < 2k. In all of the situations, we investigate the constructions of the graphs obtained

Using clustering of rankings to explain brand preferences with personality and socio-demographic variables

The primary aim of market segmentation is to identify relevant groups of consumers that can be addressed efficiently by marketing or advertising campaigns. This paper addresses the issue whether consumer groups can be identified from background variables that are not brand-related, and how much personality vs. socio-demographic variables contribute to the identification of consumer clusters. This is done by clustering aggregated preferences for 25 brands across 5 different product categories, and by relating socio-demographic and personality variables to the clusters using logistic regression and random forests over a range of different numbers of clusters. Results indicate that some personality variables contribute significantly to the identification of consumer groups in one sample. However, these results were not replicated on a second sample that was more heterogeneous in terms of socio-demographic characteristics and not representative of the brands target audience

Rights and Wrongs in Scholarly Understanding of the Topic of North Africa and the Holocaust

Abstract The Holocaust and its impact are by now a vast interdisciplinary field of research that is carried out across the globe. Recently, growing attention has been paid to the fate of North African Jewry during the Holocaust period. The volume under review, based on papers from a 2015 conference on this subject at UCLA, raises some essential questions regarding the history and present state of research in this field. The review closely and critically examines the various chapters, which from the perspective of scholarly quality range from excellent to frustrating. This article elaborates on essential issues from the perspective of the broader field of Holocaust historiography: conceptualization of “the Holocaust” and what is part of it and what is not; the evolution of Holocaust historiography in general and as relating to North Africa; and knowledge by scholars in this field of the broader picture of the Holocaust, especially the evolution of anti-Jewish policies. The conclusion is that research has to be done with an awareness of the multifacetedness of the Holocaust and without simplistic generalizations and trivializations.</jats:p