Paired-domination in generalized claw-free graphs

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998) 199–206). A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The paired-domination number of G, denoted by , is the minimum cardinality of a paired-dominating set of G. If G does not contain a graph F as an induced subgraph, then G is said to be F-free. Haynes and Slater (Networks 32 (1998) 199–206) showed that if G is a connected graph of order , then and this bound is sharp for graphs of arbitrarily large order. Every graph is -free for some integer a ≥ 0. We show that for every integer a ≥ 0, if G is a connected -free graph of order n ≥ 2, then with infinitely many extremal graphs.     

Uncertainty Quantification in the Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) provides an approximate, sequential Monte Carlo solution to the recursive data assimilation algorithm for hidden Markov chains. The challenging conditioning step is approximated by a linear updating, and the updating weights, termed Kalman weights, are inferred from the ensemble members. The EnKF scheme is known to provide unstable predictions and to underestimate the prediction intervals, and even sometimes to diverge. The underlying cause for these shortcomings is poorly understood. We find that the ensemble members couple in the conditioning procedure and that the coupling increase multiplicatively in the recursive conditioning steps. Under reasonable Gauss‐independence assumptions, exact expressions for this correlation are developed. Moreover, expressions for the precision of the predictions and the downward bias in the empirical variance introduced in one conditioning step are found. These results are confirmed by a Gauss‐linear simulation study. Furthermore, we quantitatively evaluate an alternative, improved EnKF scheme on the basis of transformations of ensemble members under the same Gauss‐independent assumptions. The scheme is compared with the frequently used ensemble inflation scheme.     

Leaving the Nordic Path? The Changing Role of Danish Trade Unions in the Welfare Reform Process

For a long period, Denmark has been labeled a ‘model country’ with a comprehensive welfare state and a successful model of corporatist policy‐making. Danish unions are considered amongst the strongest in the world, and they have for a long time been a distinct part of the political system, and as social partners, they were strongly integrated into decision‐making processes. The analysis of the Danish welfare and labour market policy during the last two decades documents a profound change in the arrangement and in the status of the social partners (especially unions) in the Danish political system. The results show that two important pillars of the Danish model – the social partner basis and the collective trust in partnership – are eroding. Unions are no longer part of the law‐making process and, since 2007, they are formally excluded from the organization of the decision‐making process. Recent developments point at weaker unions that operate more as lobbyists instead of being strong corporatist institutions or part of the decision‐making process. The results of the study are thought‐provoking and the basis for a revised thinking of the Danish and the Nordic model.     

A comparison of male and female dually arrested domestic violence offenders

This research provides information on dually arrested female defendants in domestic violence cases. The data comes from all heterosexual domestic violence cases resulting in a dual arrest from one large mid-South city during a 28-month period. Information on matched pairs of dually arrested male and female defendants (N = 317) came from multiple sources, including official criminal justice records (arrest reports and local criminal histories) as well as victim/offender interviews with both the arrestee and his/her partner. Comparisons were made between males and females in terms of their demographics, criminal histories, prior history of domestic violence (as both victim and offender), and behavior during the instant offense. Analyses revealed that these couples had ample contact, whether as victim or offender, with the criminal justice system. While there were no significant differences in partners' reports of minor and severe physical abuse, criminal justice date indicated that male arrestees demonstrated a significantly higher overall level of severity of violence than their female counterparts. Additionally, male arrestees had a more serious history of intimate partner and extrafamilial violence as well as other indicators of an antisocial lifestyle in comparison to female arrestees. To the extent that females in our cohort demonstrated less overall criminality and engaged in less severe domestic aggression, the idea of equivalency of violence between male and female arrestees must remain questionable.     

Which trees have a differentiating-paired dominating set?

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater (Networks 32 (1998), 199–206). A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. The set S is called a differentiating-paired dominating set if for every pair of distinct vertices u and v in V(G), N[u]∩S≠N[v]∩S, where N[u] denotes the set consisting of u and all vertices adjacent to u. In this paper, we provide a constructive characterization of trees that do not have a differentiating-paired dominating set.     

Paired versus double domination in K 1,r -free graphs

A vertex in G is said to dominate itself and its neighbors. A subset S of vertices is a dominating set if S dominates every vertex of G. A paired-dominating set is a dominating set whose induced subgraph contains a perfect matching. The paired-domination number of a graph G, denoted by γ _pr(G), is the minimum cardinality of a paired-dominating set in G. 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 claw-free graph is a graph that does not contain K _1,3 as an induced subgraph. Chellali and Haynes (Util. Math. 67:161–171, 2005) showed that for every claw-free graph G, we have γ _pr(G)≤γ _×2(G). In this paper we extend this result by showing that for r≥2, if G is a connected graph that does not contain K _1,r as an induced subgraph, then $\gamma_{\mathrm{pr}}(G)\le ( \frac{2r^{2}-6r+6}{r(r-1)} )\gamma_{\times2}(G)$ .     

k-tuple total domination in cross products of graphs

For k??1 an integer, a set S of vertices in a graph G with minimum degree at least?k is a k-tuple total dominating set of G if every vertex of G is adjacent to at least k vertices in S. The minimum cardinality of a k-tuple total dominating set of G is the k-tuple total domination number of G. When k=1, the k-tuple total domination number is the well-studied total domination number. In this paper, we establish upper and lower bounds on the k-tuple total domination number of the cross product graph G×H for any two graphs G and H with minimum degree at least?k. In particular, we determine the exact value of the k-tuple total domination number of the cross product of two complete graphs.     

Independent domination in subcubic graphs

Journal of Combinatorial Optimization - A set S of vertices in a graph G is a dominating set if every vertex not in S is adjacent to a vertex in S. If, in addition, S is an independent...