We study upper and lower bounds on the kernel size for the 3-hitting set problem on hypergraphs of degree at most 3, denoted 33-hs. We first show that, unless P=NP, 3-3-hs on 3-un...
This paper considers the problem of calculating dominating sets in networks with bounded degree. In these networks, the maximal degree of any node is bounded by Δ, which is usuall...
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...
We say a countable model A has a 0-basis if the types realized in A are uniformly computable. We say A has a (d-)decidable copy if there exists a model B = A such that the element...
We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model [10]. We give a property tester that given a graph with degree bound d, an ex...