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A generalized Petersen graph GP (n, k) is a regular cubic graph on 2n vertices (the parameter k is used to define some of the edges). It was previously shown (Ball et al., 2015) that the cop number of GP (n, k) is at most 4, for all permissible values of n and k. In this paper we prove that the cop number of "most" generalized Petersen graphs is exactly 4. More precisely, we show that unless n and k fall into certain specified categories, then the cop number of GP (n, k) is 4. The graphs to which our result applies all have girth 8.In fact, our argument is slightly more general: we show that in any cubic graph of girth at least 8, unless there exist two cycles of length 8 whose intersection is a path of length 2, then the cop number of the graph is at least 4. Even more generally, in a graph of girth at least 9 and minimum valency δ, the cop number is at least δ + 1.

BACKGROUND Emergency medical services (EMS) assessment and presentation to the emergency department (ED) for syncope (fainting) often results in hospital admission and costly diagnostic testing that rarely benefits patients. Protocols that support paramedics to assess, treat and refer low-risk syncope may allow for ED transport of only high-risk patients. The development and successful uptake of such protocols is limited by a dearth of information about factors patients consider when deciding to seek EMS care following syncope. OBJECTIVE We aimed to explore decision-making processes of individuals with syncope when deciding whether (or not) to call EMS after fainting as a starting point in the development of prehospital risk-stratification protocols. METHODS Twenty-five adults (aged 18–65 years) with a history of ≥ 1 syncopal episode were recruited across four Canadian provinces. Individual semi-structured interviews were conducted, recorded, and transcribed. Straussian grounded theory methods were used to identify common themes and a core (overarching) category. RESULTS Four common themes were identified: (a) previous experiences with the healthcare system (e.g., feeling dismissed), (b) individual patient factors (e.g., age, comorbidities), (c) attitudes and beliefs (e.g., concerns about burdening the health care system, believing syncope is “not serious enough” to seek care), and (d) contextual factors (i.e., influence of important others, symptom severity). Perceived judgement of the patient by EMS was identified as the overarching core category that influenced patients’ decision-making to seek care. CONCLUSION The decision to seek EMS care after syncope is a complex process involving patient consideration of past experiences, pre-existing attitudes and beliefs, and individual- and contextual factors. Patients’ previous experiences of judgement and dismissal by EMS for fainting may interfere with patient receptiveness to traditional EMS protocols for syncope. These barriers could be targets for training and education for paramedics and help to inform the development of prehospital protocols to improve care and satisfaction among patients with syncope.