All-fault-tolerant embedding of a complete binary tree in a group of Cayley graphs

1996 ◽  
Vol 143 (2) ◽  
pp. 156 ◽  
Author(s):  
C.-C. Hsu
Keyword(s):  
Binary Tree ◽  
Fault Tolerant ◽  
Cayley Graphs ◽  
Complete Binary Tree

Binary Trees and the n-Cutset Property

1991 ◽  
Vol 34 (1) ◽  
pp. 23-30 ◽  
Author(s):  
Peter Arpin ◽  
John Ginsburg
Keyword(s):  
Positive Integer ◽  
Partially Ordered Set ◽  
Binary Tree ◽  
Ordered Set ◽  
Maximal Chain ◽  
Binary Trees ◽  
Complete Binary Tree ◽  
Maximal Elements ◽  
Extremal Case ◽  
Result Theorem

AbstractA partially ordered set P is said to have the n-cutset property if for every element x of P, there is a subset S of P all of whose elements are noncomparable to x, with |S| ≤ n, and such that every maximal chain in P meets {x} ∪ S. It is known that if P has the n-cutset property then P has at most 2n maximal elements. Here we are concerned with the extremal case. We let Max P denote the set of maximal elements of P. We establish the following result. THEOREM: Let n be a positive integer. Suppose P has the n-cutset property and that |Max P| = 2n. Then P contains a complete binary tree T of height n with Max T = Max P and such that C ∩ T is a maximal chain in T for every maximal chain C of P. Two examples are given to show that this result does not extend to the case when n is infinite. However the following is shown. THEOREM: Suppose that P has the ω-cutset property and that |Max P| = 2ω. If P — Max P is countable then P contains a complete binary tree of height ω

Two Models of Additional Adjacencies between the Root and Descendants in a Complete Binary Tree Minimizing Total Path Length

2009 ◽  
Author(s):  
Kiyoshi Sawada ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
Osca Castillo ◽  
...  
Keyword(s):  
Binary Tree ◽  
Path Length ◽  
Complete Binary Tree ◽  
Total Path Length
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