Additive combinatorics and graph theory

2018 ◽  
pp. 685-716
Author(s):  
Endre Szemerédi
Keyword(s):  
Graph Theory ◽  
Additive Combinatorics

scholarly journals Short Proofs of Some Extremal Results

2013 ◽  
Vol 23 (1) ◽  
pp. 8-28 ◽  
Author(s):  
DAVID CONLON ◽  
JACOB FOX ◽  
BENNY SUDAKOV
Keyword(s):  
Graph Theory ◽  
Ramsey Theory ◽  
Extremal Graph ◽  
Extremal Graph Theory ◽  
Extremal Combinatorics ◽  
Additive Combinatorics ◽  
Open Problems

We prove several results from different areas of extremal combinatorics, giving complete or partial solutions to a number of open problems. These results, coming from areas such as extremal graph theory, Ramsey theory and additive combinatorics, have been collected together because in each case the relevant proofs are quite short.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

Application of Graph Theory in Social Media

2018 ◽  
Vol 6 (10) ◽  
pp. 722-729 ◽  
Author(s):  
Anwesha Chakraborty ◽  
Trina Dutta ◽  
Sushmita Mondal ◽  
Asoke Nath
Keyword(s):  
Social Media ◽  
Graph Theory
Sign in / Sign up

Export Citation Format

Share Document