منابع مشابه
Spanning trees of countable graphs omitting sets of dominated ends
Generalizing the well-known theorem of Halin (1964) that a countable connected graph G contains an end-faithful spanning tree (i.e., an end-preserving tree that omits no end of G), we establish some results about the existence of end-preserving spanning trees omitting some prescribed set of ends. We remark that if such a tree exists, the omitted ends must all be dominated, and even then counter...
متن کاملEnds in Uniform Spanning Forests
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience. §
متن کاملSpanning Trees in 2-trees
A spanning tree of a graph G is a connected acyclic spanning subgraph of G. We consider enumeration of spanning trees when G is a 2-tree, meaning that G is obtained from one edge by iteratively adding a vertex whose neighborhood consists of two adjacent vertices. We use this construction order both to inductively list the spanning trees without repetition and to give bounds on the number of the...
متن کاملEnds in Uniform Spanning Forests 1
It has hitherto been known that in a transitive unimodular graph, each tree in the wired spanning forest has only one end a.s. We dispense with the assumptions of transitivity and unimodularity, replacing them with a much broader condition on the isoperimetric profile that requires just slightly more than uniform transience.
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90455-o