2-Colorings of Hypergraphs with Large Girth.

Demidovich, Yu. A.

A hypergraph has property if there exists a 2-coloring of the set such that each edge contains at least vertices of each color. We let and , respectively, denote the least number of edges of an -homogeneous hypergraph without property which contains either no cycles of length at least or no two edges intersecting in more than vertices. In the paper, upper bounds for these quantities are given. As a consequence, we obtain results for , i.e., for the least number of edges of an -homogeneous simple hypergraph without property . Let be the maximal degree of vertices of a hypergraph . By we denote the minimal degree such that there exists an -homogeneous hypergraph with maximal degree and girth at least but without property . In the paper, an upper bound for is obtained.

HYPERGRAPHS; EDGES (Geometry)

Mathematical Notes, 2020, Vol 108, Issue 1/2, p188

0001-4346

Academic Journal

10.1134/S0001434620070202