Recent empirical evaluations of exact algorithms for Feedback Vertex Set have demonstrated the efficiency a highest-degree branching algorithm with degree-based pruning. In this paper, we prove that empirically fast runs in $$O(3.460^k n)$$ time, where k is solution size. This improves previous best $$O(3.619^k -time deterministic obtained by Kociumaka and Pilipczuk (Inf Process Lett 114:556–56...

Sacks [Sa1966a] asks if the metarecursively enumerable degrees are elementarily equivalent to the r.e. degrees. In unpublished work, Slaman and Shore proved that they are not. This paper provides a simpler proof of that result and characterizes the degree of the theory as O(ω) or, equivalently, that of the truth set of LωCK 1 .

Abstract We study subfields of quotient division algebras of domains of finite GK dimension and introduce a combinatorial property we call the straightening property. We show that many classes of algebras have this straightening property and show that if A is a domain of GK dimension d with this property that is not PI, then the maximal subfields of the quotient division algebra of A have trans...

It is shown that the lower irredundance number and secure domination number of an n vertex tree T with maximum degree 3, are bounded below by 2(n+ 1)/(2 + 3) (T = K1, ) and ( n+ − 1)/(3 − 1), respectively. The bounds are sharp and extremal trees are exhibited. © 2006 Elsevier B.V. All rights reserved. MSC: 05C69

In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V (G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ×2(G). A function f(p) is defined, and it is shown that γ×2(G) = min f(p), where the minimum is taken over the n-dimensional cube C = {p = (p1, . . ....