From the 1 of 5 linked papers with an AI index.
6 papers
Even smaller universal posets
József Balogh, Ramon I. Garcia, Marcelo Sales
The paper proves that for any small ε>0 and large n there exists a poset of size 2^{(1+ε)n/2} that contains every n‑element poset as an induced subposet, improving previous bounds…
Improving Uniquely Decodable Codes in Binary Adder Channels
József Balogh, The Nguyen, Patric R. J. Ostergard +2
We present a general method to modify existing uniquely decodable codes in the -user binary adder channel. If at least one of the original constituent codes does not have averag…
Packing edge disjoint cliques in graphs
József Balogh, Michael C. Wigal
Let be fixed and be an -vertex graph. A long-standing conjecture of GyÅri states that if , where denotes the number of edges o…
Clique covers and decompositions of cliques of graphs
József Balogh, Jialin He, Robert A. Krueger +2
In 1966, ErdÅs, Goodman, and Pósa showed that if is an -vertex graph, then at most cliques of are needed to cover the edges of , and the bou…
On the number of -free set systems for tree posets
József Balogh, Ramon I. Garcia, Michael C. Wigal
We say a finite poset is a tree poset if its Hasse diagram is a tree. Let be the length of the largest chain contained in . We show that when is a fixed tree poset,…
Grid-drawings of graphs in three-dimensions
Jozsef Balogh, Ethan Patrick White
Using probabilistic methods, we obtain grid-drawings of graphs without crossings with low volume and small aspect ratio. We show that every -degenerate graph on vertices can…