Displaying similar documents to “Simplicity of Neretin's group of spheromorphisms”

Multi-faithful spanning trees of infinite graphs

Norbert Polat (2001)

Czechoslovak Mathematical Journal

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For an end τ and a tree T of a graph G we denote respectively by m ( τ ) and m T ( τ ) the maximum numbers of pairwise disjoint rays of G and T belonging to τ , and we define t m ( τ ) : = min { m T ( τ ) T is a spanning tree of G } . In this paper we give partial answers—affirmative and negative ones—to the general problem of determining if, for a function f mapping every end τ of G to a cardinal f ( τ ) such that t m ( τ ) ≤ f ( τ ) ≤ m ( τ ) , there exists a spanning tree T of G such that m T ( τ ) = f ( τ ) for every end τ of G .

Pressing Down Lemma for λ -trees and its applications

Hui Li, Liang-Xue Peng (2013)

Czechoslovak Mathematical Journal

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For any ordinal λ of uncountable cofinality, a λ -tree is a tree T of height λ such that | T α | < cf ( λ ) for each α < λ , where T α = { x ∈ T : ht ( x ) = α } . In this note we get a Pressing Down Lemma for λ -trees and discuss some of its applications. We show that if η is an uncountable ordinal and T is a Hausdorff tree of height η such that | T α | ≤ ω for each α < η , then the tree T is collectionwise Hausdorff if and only if for each antichain C ⊂ T and for each limit ordinal α ≤ η with cf ( α ) > ω , { ht ( c ) : c ∈ C } ∩ α is not stationary in α . In the last part of this note, we investigate...

The triangles method to build X -trees from incomplete distance matrices

Alain Guénoche, Bruno Leclerc (2001)

RAIRO - Operations Research - Recherche Opérationnelle

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A method to infer X -trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2 n -3 distance values between the n elements of X , if they fulfill some explicit conditions. This construction is based on the mapping between X -tree and a weighted generalized 2-tree spanning X .

Spanning caterpillars with bounded diameter

Ralph Faudree, Ronald Gould, Michael Jacobson, Linda Lesniak (1995)

Discussiones Mathematicae Graph Theory

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A caterpillar is a tree with the property that the vertices of degree at least 2 induce a path. We show that for every graph G of order n, either G or G̅ has a spanning caterpillar of diameter at most 2 log n. Furthermore, we show that if G is a graph of diameter 2 (diameter 3), then G contains a spanning caterpillar of diameter at most c n 3 / 4 (at most n).

Closure for spanning trees and distant area

Jun Fujisawa, Akira Saito, Ingo Schiermeyer (2011)

Discussiones Mathematicae Graph Theory

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A k-ended tree is a tree with at most k endvertices. Broersma and Tuinstra [3] have proved that for k ≥ 2 and for a pair of nonadjacent vertices u, v in a graph G of order n with d e g G u + d e g G v ≥ n - 1 , G has a spanning k-ended tree if and only if G+uv has a spanning k-ended tree. The distant area for u and v is the subgraph induced by the set of vertices that are not adjacent with u or v. We investigate the relationship between the condition on d e g G u + d e g G v and the structure of the distant area for u and v. We prove...

A remark on branch weights in countable trees

Bohdan Zelinka (2004)

Mathematica Bohemica

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Let T be a tree, let u be its vertex. The branch weight b ( u ) of u is the maximum number of vertices of a branch of T at u . The set of vertices u of T in which b ( u ) attains its minimum is the branch weight centroid B ( T ) of T . For finite trees the present author proved that B ( T ) coincides with the median of T , therefore it consists of one vertex or of two adjacent vertices. In this paper we show that for infinite countable trees the situation is quite different.