Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each c...Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each color appears at each vertex v at least f（v） times. Let X＇fc（G） be the maximum positive integer k for which an f-edge cover-coloring with k colors of G exists. In this paper, we give a new lower bound of X＇fc（G）, which is sharp.展开更多
An f-edge cover-colouring of a graph G = (V, E) is an assignment of colours to the edges of G such that every colour appears at each vertex v ∈ V at least f(v) times. The maximum number of colours needed to f-edge co...An f-edge cover-colouring of a graph G = (V, E) is an assignment of colours to the edges of G such that every colour appears at each vertex v ∈ V at least f(v) times. The maximum number of colours needed to f-edge cover colour G is called the f-edge cover chromatic index of G, denoted by Xfc(G). This paper gives that min[d(v)-1/f(v)]≤xfc(G)≤展开更多
OBJECTIVE The clinical use of PET/CT in oncology has led to the realization that 18F-FDG uptake in brown adipose tissue(BAT) can be a common cause of potentially misleading false-positive PET scans.The goal of this st...OBJECTIVE The clinical use of PET/CT in oncology has led to the realization that 18F-FDG uptake in brown adipose tissue(BAT) can be a common cause of potentially misleading false-positive PET scans.The goal of this study was to study 18F-FDG uptake in cervical and supraclavicular regions and its characteristics with PET/CT.METHODSAll the PET/CT scans obtained at our institutionfrom July 2007 to January 2008 were retrospectively reviewed forincreased 18F-FDG uptake in BAT.The cases in which increased18F-FDG in cervical and supraclavicular regions was not localizedto a so -tissue mass or lymph node or muscle on the CT images,were included in this study.The following features were recorded:body weight,body mass index(BMI) and maximal standardizeduptake value(SUVmax).In these selected patients,the BAT uptake in other area of the body was also recorded.RESULTS PET/CT scans were obtained in 457 patients(259 males and 198 females).In all of the scans,cervical and supraclavicular BAT uptake was observed in 12 patients(2 males and 10 females) and was typically bilateral,symmetric and intense.The range of the SUVmax was 3.6～12.82(mean 6.9 ± 2.6).BAT uptake was more common in females than in males,showing a significant difference(P = 0.004).Although 18F-FDG uptake in BAT occurred more o en in underweight patients with low BMI,there was no difference in the body weight(P = 0.607) or BMI(P = 0.491) of these patients with hypermetabolic BAT compared with controls.CONCLUSION Hypermetabolic BAT uptake can be localized in cervical and supraclavicular regions with it occurring more commonly in females compared to males.Knowledge of this potential pitfall with PET/CT is important in improving diagnostic interpretation and accurate staging.展开更多
Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equi...Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by the authors are given. Some new problems and conjectures are presented.展开更多
文摘Let G be a multigraph with vertex set V（G）. Assume that a positive integer f（v） with 1 ≤ f（v） ≤ d（v） is associated with each vertex v ∈ V. An edge coloring of G is called an f-edge cover-coloring, if each color appears at each vertex v at least f（v） times. Let X＇fc（G） be the maximum positive integer k for which an f-edge cover-coloring with k colors of G exists. In this paper, we give a new lower bound of X＇fc（G）, which is sharp.
文摘An f-edge cover-colouring of a graph G = (V, E) is an assignment of colours to the edges of G such that every colour appears at each vertex v ∈ V at least f(v) times. The maximum number of colours needed to f-edge cover colour G is called the f-edge cover chromatic index of G, denoted by Xfc(G). This paper gives that min[d(v)-1/f(v)]≤xfc(G)≤
文摘OBJECTIVE The clinical use of PET/CT in oncology has led to the realization that 18F-FDG uptake in brown adipose tissue(BAT) can be a common cause of potentially misleading false-positive PET scans.The goal of this study was to study 18F-FDG uptake in cervical and supraclavicular regions and its characteristics with PET/CT.METHODSAll the PET/CT scans obtained at our institutionfrom July 2007 to January 2008 were retrospectively reviewed forincreased 18F-FDG uptake in BAT.The cases in which increased18F-FDG in cervical and supraclavicular regions was not localizedto a so -tissue mass or lymph node or muscle on the CT images,were included in this study.The following features were recorded:body weight,body mass index(BMI) and maximal standardizeduptake value(SUVmax).In these selected patients,the BAT uptake in other area of the body was also recorded.RESULTS PET/CT scans were obtained in 457 patients(259 males and 198 females).In all of the scans,cervical and supraclavicular BAT uptake was observed in 12 patients(2 males and 10 females) and was typically bilateral,symmetric and intense.The range of the SUVmax was 3.6～12.82(mean 6.9 ± 2.6).BAT uptake was more common in females than in males,showing a significant difference(P = 0.004).Although 18F-FDG uptake in BAT occurred more o en in underweight patients with low BMI,there was no difference in the body weight(P = 0.607) or BMI(P = 0.491) of these patients with hypermetabolic BAT compared with controls.CONCLUSION Hypermetabolic BAT uptake can be localized in cervical and supraclavicular regions with it occurring more commonly in females compared to males.Knowledge of this potential pitfall with PET/CT is important in improving diagnostic interpretation and accurate staging.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos. 10871119, 10971121 and Quality Control Standards on Undergraduate Medical Education under Grant No. 200804220001.
文摘Graph coloring has interesting real life applications in optimization and network design. In this paper some new results on the acyclic-edge coloring, f-edge coloring, g-edge cover coloring, （g, f）-coloring and equitable edge-coloring of graphs are introduced. In particular, some new results related to the above colorings obtained by the authors are given. Some new problems and conjectures are presented.
