Uniform hypergraphs containing no grids |
| |
Authors: | Zoltán Füredi Miklós Ruszinkó |
| |
Institution: | Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, P. O. Box 127, 1364, Hungary |
| |
Abstract: | A hypergraph is called an r×rgrid if it is isomorphic to a pattern of r horizontal and r vertical lines, i.e., a family of sets {A1,…,Ar,B1,…,Br} such that Ai∩Aj=Bi∩Bj=0? for 1≤i<j≤r and |Ai∩Bj|=1 for 1≤i,j≤r. Three sets C1,C2,C3 form a triangle if they pairwise intersect in three distinct singletons, |C1∩C2|=|C2∩C3|=|C3∩C1|=1, C1∩C2≠C1∩C3. A hypergraph is linear , if |E∩F|≤1 holds for every pair of edges E≠F. |
| |
Keywords: | 05D05 11B25 |
本文献已被 ScienceDirect 等数据库收录! |
|