This paper addresses the following questions for a given tree T and integer d 2: (1) What is the minimum number of degree-d subtrees that partition E(T)? (2) What is the minimum n...
This paper proves that for every positive integers n and k, we can explicitly construct a graph G with n+O(k) vertices and maximum degree 3, such that even after removing any k ve...
The graph inference from a walk for a class C of undirected edge-colored graphs is, given a string x of colors, nding the smallest graph G in C that allows a traverse of all edge...
We consider the problem of testing 3-colorability in the bounded-degree model. We show that, for small enough ε, every tester for 3colorability must have query complexity Ω(n)....
In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph G (linear array or mesh in this paper),...