Forcing large tight components in 3-graphs. (March 2019)

• Record Type: Journal Article
• Authors: Georgakopoulos, Agelos; Haslegrave, John; Montgomery, Richard
• Is Part Of: European journal of combinatorics. Volume 77(2019)
• Page Start: 57
• Page End: 67
• Publication Date: 2019-03
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2018.11.001
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: Any n -vertex 3-graph with minimum codegree at least ⌊ n ∕ 3 ⌋ must have a spanning tight component, but immediately below this threshold it is possible for no tight component to span more than ⌈ 2 n ∕ 3 ⌉ vertices. Motivated by this observation, we ask which codegree forces a tight component of at least any given size. The corresponding function seems to have infinitely many discontinuities, but we provide upper and lower bounds, which asymptotically converge as the function nears the origin.