(1) Background: There is a constant search for new prognostic factors that would allow us to accurately determine the prognosis, select the type of treatment, and monitor the patient diagnosed with uveal melanoma in a minimally invasive and easily accessible way. Therefore, we decided to evaluate the prognostic role of its pigmentation in a clinical assessment. (2) Methods: The pigmentation of 154 uveal melanomas was assessed by indirect ophthalmoscopy. Two groups of tumours were identified: amelanotic and pigmented. The statistical relationships between these two groups and clinical, pathological parameters and the long-term survival rate were analyzed. (3) Results: There were 16.9% amelanotic tumours among all and they occurred in younger patients (p = 0.022). In pigmented melanomas, unfavourable prognostic features such as: epithelioid cells (p = 0.0013), extrascleral extension (p = 0.027), macronucleoli (p = 0.0065), and the absence of BAP1 expression (p = 0.029) were statistically more frequently observed. Kaplan–Meier analysis demonstrated significantly better overall (p = 0.017) and disease-free (p < 0.001) survival rates for patients with amelanotic tumours. However, this relationship was statistically significant for lower stage tumours (AJCC stage II), and was not present in larger and more advanced stages (AJCC stage III). (4) Conclusions: The results obtained suggested that the presence of pigmentation in uveal melanoma by indirect ophthalmoscopy was associated with a worse prognosis, compared to amelanotic lesions. These findings could be useful in the choice of therapeutic and follow-up options in the future.
For a graph G, by χ 2 (G) we denote the minimum integer k, such that there is a k-coloring of the vertices of G in which vertices at distance at most 2 receive distinct colors. Equivalently, χ 2 (G) is the chromatic number of the square of G. In 1977 Wegner conjectured that if G is planar and has maximum degree ∆, then χ 2 (G) ≤ 7 if ∆ ≤ 3, χ 2 (G) ≤ ∆ + 5 if 4 ≤ ∆ ≤ 7, and 3∆/2 + 1 if ∆ ≥ 8. Despite extensive work, the known upper bounds are quite far from the conjectured ones, especially for small values of ∆. In this work we show that for every planar graph G with maximum degree ∆ it holds that χ 2 (G) ≤ 3∆ + 4. This result provides the best known upper bound for 6 ≤ ∆ ≤ 14.
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