The Girth-Chromatic number theorem is a theorem from graph theory, stating that graphs with arbitrarily large girth and chromatic number exist. We formalize a probabilistic proof of this theorem in the Isabelle/HOL theorem prover, closely following a standard textbook proof and use this to explore the use of the probabilistic method in a theorem prover.

We conjecture that every planar graph of odd-girth at least 11 admits a homomorphism to the Coxeter graph. Supporting this conjecture, we prove that every planar graph of odd-girth at least 17 admits a homomorphism to the Coxeter graph.

Introduction. Current girth augmentation techniques rely either on liposuction/injection or on the use of dermal fat grafts. These procedures have serious disadvantages, including regression in gained size, deformities, irregular contour, and asymmetry. Ideally, the augmentation technique should ensure durability and symmetry. This case report describes the first application of a flap (superfic...

BACKGROUND Abdominal distension is one of the cardinal features of irritable bowel syndrome (IBS) with patients often ranking it as more intrusive than their pain or bowel dysfunction. If this symptom could be quantified accurately and reliably it would provide, for the first time, an objective way of assessing this disorder. Using the principle of inductance plethysmography we have developed a...

Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H. Determining if a given graph G is the square of some graph is not easy in general. Motwani and Sudan [11] proved that it is NP-complete to determine if a given graph G is the square of some graph. The graph introduced in their ...

OBJECTIVE Abnormal imaging in the patellar tendon reveals pathology that is often associated with knee pain. Anthropometric measures of body size and mass, such as height, weight and waist-to-hip ratio (WHR), have been individually associated with abnormal imaging. The aim of this study was to investigate the anthropometric factors that have the strongest relationship with abnormal imaging in v...

We give an upper bound for the online chromatic number of graphs with high girth and for graphs with high oddgirth generalizing Kierstead’s algorithm for graphs that contain neither a C3 or C5 as an induced subgraph. keywords: online algorithms, combinatorial problems

PURPOSE Compression garments have been commonly used in a medical setting as a method to promote blood flow. Increases in blood flow during exercise may aid in the delivery of oxygen to the exercising muscles and, subsequently, enhance performance. The aim of the current study was to investigate the effect of wearing lower body compression garments during a cycling test. METHODS Twelve highly...