Hendry’s Conjecture on Chordal Graph Subclasses

A cycle is extendable if there exists another cycle on the same set of vertices plus one more vertex. G.R.T. Hendry conjectured (1990) that every non spanning cycle in a Hamiltonian chordal graph is extendable. This has recently been disproved (2015), but is still open for classes of strongly chordal graphs. Hendry’s Conjecture has been shown to hold for the following subclasses of chordal graphs: planar chordal graphs (2002), interval graphs, strongly chordal graphs with (two specific) forbidden subgraphs, split graphs (2006), and spider intersection graphs (2013). Chapter 1 of this dissertation is an introduction to the subject matter. In chapter 2 we verify that Hendry’s Conjecture holds for Ptolemaic graphs which are a subclass of strongly chordal graphs, alongside with a strong result on how smoothly the extension can happen. In chapter 3 we develop tools for working on tree representations of chordal graphs with Hendry’s Conjecture in mind. Chapter 4 is an application of these tools to interval graphs, another subclass of chordal graphs. Chapter 5 is about manipulating the aformentioned counterexample to Hendry’s Conjecture, and applying tools from chapter 3 on it. This yields information on the structure of graphs for which Hendry’s conjecture holds

Case Report Amyloid Goiter Secondary to Ulcerative Colitis

Diffuse amyloid goiter (AG) is an entity characterized by the deposition of amyloid in the thyroid gland. AG may be associated with either primary or secondary amyloidosis. Secondary amyloidosis is rarely caused by inflammatory bowel diseases. Secondary amyloidosis is relatively more common in the patients with Crohn's disease, whereas it is highly rare in patients with ulcerative colitis. Diffuse amyloid goiter caused by ulcerative colitis is also a rare condition. In the presence of amyloid in the thyroid gland, medullary thyroid cancer should be kept in mind in the differential diagnosis. Imaging techniques and biochemical tests are not very helpful in the diagnosis of secondary amyloid goiter and the definitive diagnosis is established based on the histopathologic analysis and histochemical staining techniques. In this report, we present a 35-year-old male patient with diffuse amyloid goiter caused by secondary amyloidosis associated with ulcerative colitis

Effect of the COVID-19 pandemic on surgery for indeterminate thyroid nodules (THYCOVID): a retrospective, international, multicentre, cross-sectional study

Background Since its outbreak in early 2020, the COVID-19 pandemic has diverted resources from non-urgent and elective procedures, leading to diagnosis and treatment delays, with an increased number of neoplasms at advanced stages worldwide. The aims of this study were to quantify the reduction in surgical activity for indeterminate thyroid nodules during the COVID-19 pandemic; and to evaluate whether delays in surgery led to an increased occurrence of aggressive tumours.Methods In this retrospective, international, cross-sectional study, centres were invited to participate in June 22, 2022; each centre joining the study was asked to provide data from medical records on all surgical thyroidectomies consecutively performed from Jan 1, 2019, to Dec 31, 2021. Patients with indeterminate thyroid nodules were divided into three groups according to when they underwent surgery: from Jan 1, 2019, to Feb 29, 2020 (global prepandemic phase), from March 1, 2020, to May 31, 2021 (pandemic escalation phase), and from June 1 to Dec 31, 2021 (pandemic decrease phase). The main outcomes were, for each phase, the number of surgeries for indeterminate thyroid nodules, and in patients with a postoperative diagnosis of thyroid cancers, the occurrence of tumours larger than 10 mm, extrathyroidal extension, lymph node metastases, vascular invasion, distant metastases, and tumours at high risk of structural disease recurrence. Univariate analysis was used to compare the probability of aggressive thyroid features between the first and third study phases. The study was registered on ClinicalTrials.gov, NCT05178186.Findings Data from 157 centres (n=49 countries) on 87 467 patients who underwent surgery for benign and malignant thyroid disease were collected, of whom 22 974 patients (18 052 [78 center dot 6%] female patients and 4922 [21 center dot 4%] male patients) received surgery for indeterminate thyroid nodules. We observed a significant reduction in surgery for indeterminate thyroid nodules during the pandemic escalation phase (median monthly surgeries per centre, 1 center dot 4 [IQR 0 center dot 6-3 center dot 4]) compared with the prepandemic phase (2 center dot 0 [0 center dot 9-3 center dot 7]; p<0 center dot 0001) and pandemic decrease phase (2 center dot 3 [1 center dot 0-5 center dot 0]; p<0 center dot 0001). Compared with the prepandemic phase, in the pandemic decrease phase we observed an increased occurrence of thyroid tumours larger than 10 mm (2554 [69 center dot 0%] of 3704 vs 1515 [71 center dot 5%] of 2119; OR 1 center dot 1 [95% CI 1 center dot 0-1 center dot 3]; p=0 center dot 042), lymph node metastases (343 [9 center dot 3%] vs 264 [12 center dot 5%]; OR 1 center dot 4 [1 center dot 2-1 center dot 7]; p=0 center dot 0001), and tumours at high risk of structural disease recurrence (203 [5 center dot 7%] of 3584 vs 155 [7 center dot 7%] of 2006; OR 1 center dot 4 [1 center dot 1-1 center dot 7]; p=0 center dot 0039).Interpretation Our study suggests that the reduction in surgical activity for indeterminate thyroid nodules during the COVID-19 pandemic period could have led to an increased occurrence of aggressive thyroid tumours. However, other compelling hypotheses, including increased selection of patients with aggressive malignancies during this period, should be considered. We suggest that surgery for indeterminate thyroid nodules should no longer be postponed even in future instances of pandemic escalation.Funding None.Copyright (c) 2023 Published by Elsevier Ltd. All rights reserved

Proper Connection with Many Colors

We say an edge-colored graph is properly connected if, between every pair of vertices, there exists a properly colored path. For a graph G, define the proper connection number pc(G) to be the minimum number of colors k such that there exists a k-coloring of E(G) which is properly connected. In this work, we study conditions on G which force upper bounds on pc(G)

Amyloid Goiter Secondary to Ulcerative Colitis

Diffuse amyloid goiter (AG) is an entity characterized by the deposition of amyloid in the thyroid gland. AG may be associated with either primary or secondary amyloidosis. Secondary amyloidosis is rarely caused by inflammatory bowel diseases. Secondary amyloidosis is relatively more common in the patients with Crohn’s disease, whereas it is highly rare in patients with ulcerative colitis. Diffuse amyloid goiter caused by ulcerative colitis is also a rare condition. In the presence of amyloid in the thyroid gland, medullary thyroid cancer should be kept in mind in the differential diagnosis. Imaging techniques and biochemical tests are not very helpful in the diagnosis of secondary amyloid goiter and the definitive diagnosis is established based on the histopathologic analysis and histochemical staining techniques. In this report, we present a 35-year-old male patient with diffuse amyloid goiter caused by secondary amyloidosis associated with ulcerative colitis

Proper connection of graphs

International audienc

Determining the Thyroid Gland Volume Causing Tracheal Compression: A Semiautomated 3D CT Volumetry Study

Background and objectives: Increased thyroid gland volume (TV) may bring about tracheal compression, which is one of the causes of respiratory distress. The aim of this study was to investigate the relationship between TV and the severity of tracheal compression independent of patients’ symptoms using semiautomated three-dimensional (3D) volumetry (S3DV) reconstructed from computed tomography (CT) scans. Cut-off TVs leading to different levels of tracheal narrowing were evaluated. Materials and Methods: One hundred sixty-three contrast-enhanced head and neck CT examinations were retrospectively assessed. TVs were measured by S3DV. The degree of tracheal compression was measured at the point where the greatest percent reduction in the cross-sectional area of the trachea adjacent to the thyroid gland was observed. To determine the severity of compression, the tracheal compression ratio (TCR) was defined (TCR = A1 (the narrowest cross-sectional area of trachea)/A2 (the largest cross-sectional area of trachea)). Results: The mean tracheal narrowing was 15% (TCR = 0.85 ± 0.15) in the study population. Patients with more than 15% tracheal compression had significantly higher TV values than those with less than 15% tracheal compression (p < 0.001). In addition, a significant correlation was found between TV and tracheal compression (p < 0.001). Moreover, the receiver operating characteristic (ROC) curve analysis revealed that the cut-off levels for TV that predict a tracheal narrowing of 10%, 20%, 30%, and 40% were 19.75 mL, 21.56 mL, 24.54 mL, and 30.29 mL, respectively (p < 0.05). Conclusions: This study objectively demonstrated that larger thyroid glands cause more severe compression on the trachea. The results may be helpful during the decision-making process for thyroidectomies to be performed due to compression symptoms