On n-partite tournaments with unique n-cycle

Communication assessment in real-life consultations is a complex task. Generic assessment instruments help but may also have disadvantages. The generic nature of the skills being assessed does not provide indications for context-specific behaviour required in practice situations; context influences are mostly taken into account implicitly. Our research questions are: 1. What factors do trained raters observe when rating workplace communication? 2. How do they take context factors into account when rating communication performance with a generic rating instrument? Nineteen general practitioners (GPs), trained in communication assessment with a generic rating instrument (the MAAS-Global), participated in a think-aloud protocol reflecting concurrent thought processes while assessing videotaped real-life consultations. They were subsequently interviewed to answer questions explicitly asking them to comment on the influence of predefined contextual factors on the assessment process. Results from both data sources were analysed. We used a grounded theory approach to untangle the influence of context factors on GP communication and on communication assessment. Both from the think-aloud procedure and from the interviews we identified various context factors influencing communication, which were categorised into doctor-related (17), patient-related (13), consultation-related (18), and education-related factors (18). Participants had different views and practices on how to incorporate context factors into the GP(-trainee) communication assessment. Raters acknowledge that context factors may affect communication in GP consultations, but struggle with how to take contextual influences into account when assessing communication performance in an educational context. To assess practice situations, raters need extra guidance on how to handle specific contextual factors

On the acyclic disconnection and the girth

The acyclic disconnection, (omega) over right arrow (D), of a digraph D is the maximum number of connected components of the underlying graph of D - A(D*), where D* is an acyclic subdigraph of D. We prove that (omega) over right arrow (D) >= g - 1 for every strongly connected digraph with girth g >= 4, and we show that (omega) over right arrow (D) = g - 1 if and only if D congruent to C-g for g >= 5. We also characterize the digraphs that satisfy (omega) over right arrow (D) = g - 1, for g = 4 in certain classes of digraphs. Finally, we define a family of bipartite tournaments based on projective planes and we prove that their acyclic disconnection is equal to 3. Then, these bipartite tournaments are counterexamples of the conjecture (omega) over right arrow (T) = 3 if and only if T congruent to (C) over right arrow (4) posed for bipartite tournaments by Figueroa et al. (2012). (C) 2015 Elsevier B.V. All rights reserved.Peer ReviewedPostprint (author's final draft

A revisit to Bang-Jensen-Gutin conjecture and Yeo's theorem

A path (cycle) is properly-colored if consecutive edges are of distinct colors. In 1997, Bang-Jensen and Gutin conjectured a necessary and sufficient condition for the existence of a Hamilton path in an edge-colored complete graph. This conjecture, confirmed by Feng, Giesen, Guo, Gutin, Jensen and Rafley in 2006, was laterly playing an important role in Lo's asymptotical proof of Bollob\'as-Erd\H{o}s' conjecture on properly-colored Hamilton cycles. In 1997, Yeo obtained a structural characterization of edge-colored graphs that containing no properly colored cycles. This result is a fundamental tool in the study of edge-colored graphs. In this paper, we first give a much shorter proof of the Bang-Jensen-Gutin Conjecture by two novel absorbing lemmas. We also prove a new sufficient condition for the existence of a properly-colored cycle and then deduce Yeo's theorem from this result and a closure concept in edge-colored graphs.Comment: 13 pages, 5 figure