Geodesic
On small non-uniform hypergraphs without property B
Mathematics and Education in Mathematics, Tome 52 (2023), pp. 71-75.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

For a given hypergraph H = (V, E) consider the sum q(H) of 2^{−|e|} over e ∈ E. Consider the class of hypergraphs whose smallest edge is of size n and for which every 2-colouring has a monochromatic edge. Let q(n) be the smallest value of q(H) in this class. We provide a survey of the known bounds on q(n) and make some minor refinements. За даден хиперграф H = (V, E) нека да разгледаме сумата q(H) на 2^{−|e|} върху e ∈ E. Разглеждаме класа хиперграфи, чието най-малко ребро е с тегло n и за които всяко 2-оцветяване има едноцветно ребро. Нека q(n) е най-малката стойност на q(H) в този клас. Представяме преглед на известните граници на q(n) и правим някои малки подобрения.
Keywords: non-uniform hypergraphs, hypergraph colouring, property B, 05C15, 05C65, неравномерни хиперграфи, оцветяване на хиперграфи, свойство B 
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     author = {Cherkashin, Danila},
     title = {On small non-uniform hypergraphs without property {B}},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MEM_2023_52_a4/}
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Cherkashin, Danila. On small non-uniform hypergraphs without property B. Mathematics and Education in Mathematics, Tome 52 (2023), pp. 71-75. http://geodesic.mathdoc.fr/item/MEM_2023_52_a4/