Equivalence of the filament and overlap graphs of subtrees of limited trees

The overlap graphs of subtrees of a tree are equivalent to subtree filament graphs, the overlap graphs of subtrees of a star are cocomparability graphs, and the overlap graphs of subtrees of a caterpillar are interval filament graphs. In this paper, we show the equivalence of many more classes of subtree overlap and subtree filament graphs, and equate them to classes of complements of cochordal-mixed graphs. Our results generalize the previously known results mentioned above

Games on interval and permutation graph representations

We describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph. We show that for a large class of these games, determining whether a given instance is a winning position for the next player is PSPACE-hard. In contrast, we give polynomial time algorithms for solving some versions of the games on trees

On List Coloring and List Homomorphism of Permutation and Interval Graphs

List coloring is an NP-complete decision problem even if the total number of colors is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list coloring of permutation graphs with a bounded total number of colors. More generally, we give a polynomial-time algorithm that solves the list-homomorphism problem to any fixed target graph for a large class of input graphs, including all permutation and interval graphs.&nbsp

A focus group based study of the perspectives of the Maltese population and healthcare professionals on medication wastage.

The World Health Organization states that globally more than half of all medication is inappropriately prescribed, dispensed or sold with a need to implement wastage reduction strategies. Developing processes which include behaviour change theories, such as the Theoretical Domains Framework (TDF), significantly impacts the positive implementation of evidence into healthcare practice. Objective To describe and understand the beliefs and behaviours regarding medication wastage of the Maltese public and healthcare professionals (HCPs) and to explore potential solutions. Setting: Malta. Method Five 90 min audio recorded focus groups (2 public and 3 HCPs) were conducted with a purposive sample who responded to a previous survey study and were willing to participate in focus groups in Malta. The guide was based upon the TDF with interview questions derived from findings of the questionnaire phase. Focus groups were audio recorded and transcribed verbatim. Analysis was carried using the framework approach. Main outcome measure Beliefs and behaviours regarding medication wastage and potential solutions to reduce medication wastage. Results A total of eleven pharmacists, six doctors and six members of the public consented to participate. Focus groups conducted with HCPs and the general public identified the following four key themes aligned with the TDF domains to address proposed solutions to minimise medication wastage: (1) practitioner effects; (2) patients effects; (3) political effects; (4) societal effects. Conclusion This study has employed a theoretical framework to obtain a better understanding of facilitators which require attention as part of strategic development

Complexity results on graphs with few cliques

Graphs and Algorithm