Premium
Almost partitioning 2‐colored complete 3‐uniform hypergraphs into two monochromatic tight or loose cycles
Author(s) -
Bustamante Sebastián,
Hàn Hiêp,
Stein Maya
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22417
Subject(s) - hypergraph , combinatorics , monochromatic color , mathematics , disjoint sets , colored , integer (computer science) , cover (algebra) , discrete mathematics , computer science , physics , mechanical engineering , materials science , optics , composite material , programming language , engineering
We show that for every η > 0 there exists an integer n 0 such that every 2 ‐coloring of the 3 ‐uniform complete hypergraph on n ≥ n 0 vertices contains two disjoint monochromatic tight cycles of distinct colors that together cover all but at most η n vertices. The same result holds if tight cycles are replaced by loose cycles.