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The structure of infinite Coxeter graphs whose largest eigenvalue belongs to the interval from √√5 + 2 to 3 3/√2] is investigated. In particular, such a graph is a tree, can have at most one label greater than 3 on its edges and such label does not exceed 6, can have only vertices with degree strictly less than 5, and among edges which are incident with vertex with degree 4 can be only one that is not incident with leaf. A number of other properties are also given for infinite Coxeter graphs with largest eigenvalue in the specified interval.

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The Silesian Beskids (Poland), the westernmost part of the Carpathian Mountains is an area with long pastoral tradition. For centuries sheep grazed in clearings located among forested ridges have been an integral part of the mountain landscape and pastoral customs have become essential elements of regional cultural heritage. In the chapter, the history and the current state of pastoralism in the Silesian Beskids are presented. The specific pastoral system developed in the region, based on annual migration of flocks between summer highland and winter lowland pastures is described. Local breeds and specific regional sheep products are depicted. Furthermore, the importance of pastoralism for the environment, landscape and plant biodiversity is analysed and efforts to recover sheep grazing in the mountains after a period of a deep recession caused by social and economic transitions connected with the collapse of the communist system are presented. The approach to restoration of pastoralism is illustrated using a case study of a pastoral centre which combines traditional sheep grazing with cheese production, education and several activities to promote pastoral tradition.

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