Fault-Tolerant Meshes with Constant Degree

Toshinori YAMADA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.4   pp.935-940
Publication Date: 2005/04/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.4.935
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 17th Workshop on Circuits and Systems in Karuizawa)
Category: 
Keyword: 
fault-tolerant graph,  dipath,  mesh,  tower graph,  constant degree,  

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Summary: 
This paper proves that for every positive integers n,k and any positive number ε, we can explicitly construct a DAG G with n+O(k1+ε) vertices and a constant degree such that even after removing any k vertices from G, the remaining digraph still contains an n-vertex dipath. This paper also proves that for every positive integers n,k and any positive number ε, we can explicitly construct a graph H with n+O(k2+ε) vertices and a constant degree such that even after removing any k vertices from H, the remaining graph still contains an n-vertex 2-dimensional square mesh.