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This is done by proving that a well-known method, the construction of a Perron Tree, can be applied to a larger collection of subsets of the unit circle than was earlier known.
      
If a collection of subsets are chosen at random from the power set of a finite setX, we give the probability that the collection is a tree of subsets ofX.
      
Given a complete graph with vertex setX and subsetsX1,X2,…,Xn, the problem of finding a subgraphG with minimum number of edges such that for everyi=1,2,…,n, G contains a spanning tree onXi, arises in the design of vacuum systems.
      
The paper proves that if G is a k-tree, then the bandwidth B of the complement of G is given by
      
In this paper the choosability of outerplanar graphs, 1-tree and strong 1-outerplanar graphs have been described completely.
      
A Halin map is a kind of planar maps oriented by a tree.
      
There is a single good at each node in the event tree.
      
Chain recurrent points and topological entropy of a tree map
      
Let f be a tree map, P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f.
      
In this paper, the notion of division for invariant closed subsets of a tree map is introduced.
      
Two feedback problems for graphs with bounded tree-width
      
Many difficult (often NP-complete) optimization problems can be solved efficiently on graphs of small tree-width with a given tree-decomposition.
      
In this paper, it is discussed how to solve the minimum feedback vertex set problem and the minimum vertex feedback edge set problem efficiently by using dynamic programming on a tree-decomposition.
      
Also for the case of t = 3, if G is non-regular, it is found that G has diameter 2 and girth at most 5 if G is not a tree.
      
The monochromatic tree partition problem is to find the minimum number of vertex disjoint monochromatic trees to cover the all vertices of G.
      
Then, its reachability tree was generated to record all reachable relations between propositions in RBS.
      
A method for detecting code security vulnerability based on variables tracking with validated-tree
      
The concept of validated tree is developed to track variables referenced by database operations in scripts.
      
It is composed of an age-implicit tree model, a diameter-related survival rate model, a recruitment model based on age and number of plots, and an area model.
      
These points can be estimated by introducing the soil factor (Ks) and tree species factor (Kt) to potential evapotranspiration with the Penman formula.
      
 

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