The size-Ramsey number R̂(F ) of a graph F is the smallest integer m such that there exists a graph G on m edges with the property that any colouring of the edges of G with two colours yields a monochromatic copy of F . In this paper, first we focus on the size-Ramsey number of a path Pn on n vertices. In particular, we show that 5n/2 − 15/2 ≤ R̂(Pn) ≤ 74n for n sufficiently large. (The upper bou...

We show that any complete k-partite graph G on n vertices, with k ≥ 3, whose edges are two-coloured, can be covered by two vertex-disjoint monochromatic paths of distinct colours, under the necessary assumption that the largest partition class of G contains at most n/2 vertices. This extends known results for complete and complete bipartite graphs. Secondly, we show that in the same situation, ...

Schematic eye models have typically been used to explain the average monochromatic and chromatic imaging properties of the eye. Both monochromatic aberrations and transverse chromatic aberration are known to vary widely across subjects. However, to our knowledge, the ability of schematic eye models to predict these individual variations has not been tested experimentally. We used a spatially re...

BACKGROUND AND PURPOSE Dual-energy CT is not used routinely for evaluation of the head and neck, and there is no consensus on the optimal virtual monochromatic image energies for evaluating normal tissues or head and neck cancer. We performed a quantitative evaluation to determine the optimal virtual monochromatic images for visualization of normal tissues, head and neck squamous cell carcinoma...

We show some consequences of results of Gallai concerning edge colorings of complete graphs that contain no tricolored triangles. We prove two conjectures of Bialostocki and Voxman about the existence of special monochromatic spanning trees in such colorings. We also determine the size of largest monochromatic stars guaranteed to occur. 2004 Wiley Periodicals, Inc. J Graph Theory 46: 211–216, 2004

We show that for any 2-local colouring of the edges of a complete bipartite graph, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any complete or complete bipartite r-locally coloured graph with O(r) disjoint monochromatic cycles. MSC: 05C38, 05C55.

Erdős-Szekeres theorem is one of classic results in combinatorial geometry. In this project we consider the colored version of the problem. Especially, we are interested in the number of empty monochromatic triangles and the existence of an empty monochromatic convex quadrilateral. We give some minor results and plausible ideas to solve the problems.

PURPOSE The purpose of this study was to evaluate image quality and status of lymph nodes in laryngeal and hypopharyngeal squamous cell carcinoma (SCC) patients using spectral CT imaging. MATERIALS AND METHODS Thirty-eight patients with laryngeal and hypopharyngeal SCCs were scanned with spectral CT mode in venous phase. The conventional 140-kVp polychromatic images and one hundred and one se...

It is well-known that in every k-coloring of the edges of the complete graph Kn there is a monochromatic connected component of order at least n k−1 . In this paper we study an extension of this problem by replacing complete graphs by graphs of large minimum degree. For k = 2 the authors proved that δ(G) > 3n 4 ensures a monochromatic connected component with at least δ(G) + 1 vertices in every...

OBJECTIVE To evaluate the clinical value of using monochromatic images in spectral CT pulmonary angiography to improve image quality of bronchial arteries. METHODS We retrospectively analyzed the chest CT images of 38 patients who underwent contrast-enhanced spectral CT. These images included a set of 140kVp polychromatic images and the default 70keV monochromatic images. Using the standard G...