The Zarankiewicz number z ( m, n ; s, t ) is the maximum number of edges in a subgraph of K m,n that does not contain K s,t as a subgraph. The bipartite Ramsey number b ( n 1 , · · · , n k ) is the least positive integer b such that any coloring of the edges of K b,b with k colors will result in a monochromatic copy of K n i ,n i in the i -th color, for some i , 1 ≤ i ≤ k . If n i = m for all i , then we denote this number by b k ( m ). In this paper we obtain the exact values of some Zarankiewicz numbers for quadrilateral ( s = t = 2), and we derive new bounds for diagonal multicolor bipartite Ramsey numbers avoiding quadrilateral. In particular, we prove that b 4 (2) = 19, and establish new general lower and upper bounds on b k (2).
Authors
- dr Janusz Dybizbański,
- Tomasz Dzido,
- Stanisław Radziszowski link open in new tab
Additional information
- Category
- Publikacja w czasopiśmie
- Type
- artykuł w czasopiśmie wyróżnionym w JCR
- Language
- angielski
- Publication year
- 2015
