Plasma and urine concentrations of Na+, K+, and urea were examined in hibernating, hypothermic, and normothermic hamsters. Plasma Na+ and K+ appear unaffected by 48 h of hypothermia (T-re 7 degrees C); however, plasma Na+ increased (P smaller than 0.05) from control values of 125.8 plus or minus 10.2 to 173 plus or minus 9.2 meg/liter in hibernators. Plasma K+ of the hibernator increased to 9.6...

For α : N→ R, an α-approximate bi-kernel is a polynomial-time algorithm that takes as input an instance (I, k) of a problem Q and outputs an instance (I ′, k′) of a problem Q′ of size bounded by a function of k such that, for every c ≥ 1, a c-approximate solution for the new instance can be turned into a c · α(k)-approximate solution of the original instance in polynomial time. This framework o...

For a graph G, let σ̄k+3(G) = min {d(x1) + d(x2) + · · · + d(xk+3) − |N(x1) ∩ N(x2) ∩ · · · ∩ N(xk+3)| | x1, x2, · · · , xk+3 are k + 3 independent vertices in G}. In [5], H. Li proved that if G is a 3-connected graph of order n and σ̄4(G) ≥ n+3, then G has a maximum cycle such that each component of G−C has at most one vertex. In this paper, we extend this result as follows. Let G be a (k + 2)-c...

A set D of vertices in a graph G is a distance-k dominating set if every vertex of G either is in D or is within distance k of at least one vertex in D. A distance-k dominating set of G of minimum cardinality is called a minimum distance-k dominating set of G. For any graph G and for a subset F of the edge set of G the set F is an edge dominating set of G if every edge of G either is in D or is...

We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a minor. In other words, we give polynomial time algorithms that, for a given H-minor free graph G and positive integer k, output an H-minor free graph G′ on O(k) vertices such that G has a (connected) dominating set of size k if and only if G′ has. Prior to our work,...

Given a clique-width expression of a graph G of clique-width k, we provide 2O(k) ·nO(1) time algorithms for connectivity constraints on locally checkable properties such as Connected Dominating Set, Connected Perfect Dominating Set or Node-Weighted Steiner Tree. We also propose an 2O(k) ·nO(1) time algorithm for Feedback Vertex Set. The best running times for all the considered cases were eithe...

In this paper, we study a generalization of the paired domination number. Let G= (V ,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a k-distance paired dominating set of G if D is a k-distance dominating set of G and the induced subgraph 〈D〉 has a perfect matching. The k-distance paired domination number p(G) is the cardinality of a smallest k-distance paired dominating set of G. ...

A k-majority tournament T on a finite vertex set V is defined by a set of 2k − 1 linear orderings of V , with u→ v if and only if u lies above v in at least k of the orders. Motivated in part by the phenomenon of “non-transitive dice”, we let F (k) be the maximum over all k-majority tournaments T of the size of a minimum dominating set of T . We show that F (k) exists for all k > 0, that F (2) ...

Top-k dominating queries combine the natural idea of selecting the k best items with a comprehensive “goodness” criterion based on dominance. A point p1 dominates p2 if p1 is as good as p2 in all attributes and is strictly better in at least one. Existing works address the problem in settings where data objects are multidimensional points. However, there are domains where we only have access to...