a b s t r a c tWe consider the variant of the minimum vertex cover problem in which we require that the cover induces a connected subgraph. We give new approximation results for this problem in dense graphs, in which either the minimum or the average degree is linear. In particular, we prove tight parameterized upper bounds on the approximation returned by Savage's algorithm, and extend a vertex cover algorithm from Karpinski and Zelikovsky to the connected case. The new algorithm approximates the minimum connected vertex cover problem within a factor strictly less than 2 on all dense graphs. All these results are shown to be tight. Finally, we introduce the price of connectivity for the vertex cover problem, defined as the worst-case ratio between the sizes of a minimum connected vertex cover and a minimum vertex cover. We prove that the price of connectivity is bounded by 2/(1 + ε) in graphs with average degree εn, and give a family of near-tight examples.

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a b s t r a c tWe analyze the simple greedy algorithm that iteratively removes the endpoints of a maximum-degree edge in a graph, where the degree of an edge is the sum of the degrees of its endpoints. This algorithm provides a 2-approximation to the minimum edge dominating set and minimum maximal matching problems. We refine its analysis and give an expression of the approximation ratio that is strictly less than 2 in the cases where the input graph has n vertices and at least n 2 edges, for > 1/2. This ratio is shown to be asymptotically tight for > 1/2.

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This article discusses the Baal-Zaphon stele, a New Kingdom funerary stele from Ugarit, depicting a certain Mamy worshipping the Levantine god Baal-Zaphon. The object, though well known since the early twentieth century, lacks a recent detailed study. A new edition of the text is proposed here, based on parallel inscriptions and on a personal inspection of the stele at the Louvre. It also incorporates a fragment mentioned in 1938 by Montet but absent from subsequent editions of the text. Finally, the article discusses the iconography of the stele, its parallels, and the ambiguous relationship between Baal and Seth.

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