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By Норман Роквелл

Замечательный альбом репродукций американского художника Нормана Роквела. Почуствуйте дух старой Америки 20-50-х годов прошлого века. Посмотрите какие живые и открытие лица!

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The maximal biconnected subgraphs of a graph are its blocks. Each edge of G falls into a single block of G, while cutvertices are shared by different blocks. The block-cutvertex tree, or BC-tree, of a connected graph G is a tree with a B-node for each block of G and a C-node for each cutvertex of G. Edges in the BC-tree connect each B-node μ to the C-nodes associated with the cutvertices in the block of μ. The BC-tree of G may be thought as rooted at a specific block ν. When the BC-tree T of a graph G is rooted at a certain block ν, we denote by G(μ) the subgraph of G induced by all vertices in the blocks contained in the subtree of T rooted at μ.

Of f2 ) not assigned to it are u∗1 and u∗2 (resp. ua and ub ), while all other vertices are assigned to such a face (Property 3). – If vertices ua and ub are both distinct from u∗1 and u∗2 and one of u∗1 and u∗2 , say u∗1 , is in f1 while the other one, say u∗2 , is in f2 , assign to f1 all vertices incident to it, except for u∗1 and ua , and assign to f2 all vertices incident to it, except for u∗2 and i (Property 1). Vertices ub . No forbidden vertex has been assigned to any face of OC ua and ub have been assigned to exactly one face.

The dyadic tree metric space can be represented as an infinite binary tree representing the x coordinates of each of its points, in which each tree node contains an interval of dyadic rational numbers; this interval of numbers is split into two halves at the two children of each node. This representation is depicted in Fig. 3, right. Our embedding begins with us finding a spanning tree T of G, choosing a root arbitrarily, and producing a heavy path decomposition of T . For technical reasons we require that each node in a nontrivial heavy path of the decomposition have at least one child that is not in the path; we add dummy nodes to T if necessary, after forming the path decomposition, to ensure that this is true.

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